Publications
Articles in Refereed Journals

A. Alphonse, Ch.M. Elliott, J. Terra, A coupled ligandreceptor bulksurface system on a moving domain: Well posedness, regularity and convergence to equilibrium, SIAM Journal on Mathematical Analysis, 50 (2018), pp. 15441592, DOI 10.1137/16M110808X .
Abstract
We prove existence, uniqueness, and regularity for a reactiondiffusion system of coupled bulksurface equations on a moving domain modelling receptorligand dynamics in cells. The nonlinear coupling between the three unknowns is through the Robin boundary condition for the bulk quantity and the right hand sides of the two surface equations. Our results are new even in the nonmoving setting, and in this case we also show exponential convergence to a steady state. The primary complications in the analysis are indeed the nonlinear coupling and the Robin boundary condition. For the well posedness and essential boundedness of solutions we use several De Giorgitype arguments, and we also develop some useful estimates to allow us to apply a Steklov averaging technique for timedependent operators to prove that solutions are strong. Some of these auxiliary results presented in this paper are of independent interest by themselves. 
A. Ceretani, C.N. Rautenberg, The Boussinesq system with mixed nonsmooth boundary conditions and ``donothing'' boundary flow, Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 14 (2019), pp. 124 (published online on 07.12.2018), DOI 10.1007/s000330181058y .
Abstract
A stationary Boussinesq system for an incompressible viscous fluid in a bounded domain with a nontrivial condition at an open boundary is studied. We consider a novel nonsmooth boundary condition associated to the heat transfer on the open boundary that involves the temperature at the boundary, the velocity of the fluid, and the outside temperature. We show that this condition is compatible with two approaches at dealing with the donothing boundary condition for the fluid: 1) the directional donothing condition and 2) the donothing condition together with an integral bound for the backflow. Wellposedness of variational formulations is proved for each problem. 
L. Adam, M. Hintermüller, Th.M. Surowiec, A PDEconstrained optimization approach for topology optimization of strained photonic devices, Annali di Matematica Pura ed Applicata. Serie Quarta. Fondazione Annali di Matematica Pura ed Applicata, c/o Dipartimento di Matematica ``U. Dini'', Firenze; SpringerVerlag, Heidelberg. English, French, German, Italian, English abstracts., 19 (2018), pp. 521557, DOI 10.1007/s1108101893945 .
Abstract
Recent studies have demonstrated the potential of using tensilestrained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multimaterial phasefield approach to determine the optimal material configuration within a socalled GermaniumonSilicon microbridge is considered. Here, an “optimal" configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the crosssection of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a nonlinear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and secondorder optimality conditions. For the numerical experiments, an array of first and secondorder solution algorithms in functionspace are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed. 
L. Adam, M. Hintermüller, Th.M. Surowiec, A semismooth Newton method with analytical pathfollowing for the $H^1$projection onto the Gibbs simplex, IMA Journal of Numerical Analysis, (2018), published online on 07.06.2018, DOI 10.1093/imanum/dry034 .
Abstract
An efficient, functionspacebased secondorder method for the $H^1$projection onto the Gibbssimplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as MoreauYosida regularization and techniques from parametric optimization. A pathfollowing technique is considered for the regularization parameter updates. A rigorous first and secondorder sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits meshindependent behavior. 
H. Antil, C. Rautenberg, Fractional elliptic quasivariational inequalities: Theory and numerics, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 20 (2018), pp. 124, DOI 10.4171/IFB/395 .

M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, A goaloriented dualweighted adaptive finite element approach for the optimal control of a nonsmooth CahnHilliardNavierStokes system, Optimization and Engineering. International Multidisciplinary Journal to Promote Optimization Theory & Applications in Engineering Sciences, 19 (2018), pp. 629662, DOI 10.1007/s1108101893936 .
Abstract
This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a timediscrete CahnHilliardNavierStokes system with variable densities. The free energy density associated to the CahnHilliard system incorporates the doubleobstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the NavierStokes equation. A dualweighed residual approach for goaloriented adaptive finite elements is presented which is based on the concept of Cstationarity. The overall error representation depends on primal residual weighted by approximate dual quantities and vice versa as well as various complementary mismatch errors. Details on the numerical realization of the adaptive concept and a report on numerical tests are given. 
M. Hintermüller, M. Holler, K. Papafitsoros, A function space framework for structural total variation regularization with applications in inverse problems, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 34 (2018), pp. 064002/1064002/39, DOI 10.1088/13616420/aab586 .
Abstract
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semicontinuous envelope (relaxation) of a suitable total variation type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted total variation for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddlepoint problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson loglikelihood data discrepancy terms. Finally, we provide proofofconcept numerical examples where we solve the saddlepoint problem for weighted TV denoising as well as for MR guided PET image reconstruction. 
M. Hintermüller, C.N. Rautenberg, N. Strogies, Dissipative and nondissipative evolutionary quasivariational inequalities with gradient constraints, SetValued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., published online on 14.07.2018, DOI 10.1007/s1122801804890 .
Abstract
Evolutionary quasivariational inequality (QVI) problems of dissipative and nondissipative nature with pointwise constraints on the gradient are studied. A semidiscretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and nondecrease in time, are derived. The proposed numerical solver reduces to a finite number of gradientconstrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints.
Contributions to Collected Editions

M. Hintermüller, T. Keil, Some recent developments in optimal control of multiphase flows, in: Shape Optimization, Homogenization and Optimal Control. DFGAIMS workshop held at the AIMS Center Senegal, March 1316, 2017, V. Schulz, D. Seck, eds., 169 of International Series of Numerical Mathematics, Birkhäuser, Springer Nature Switzerland AG, Cham, 2018, pp. 113142, DOI 10.1007/9783319904696_7 .

M. Hintermüller, A. Langer, C.N. Rautenberg, T. Wu, Adaptive regularization for image reconstruction from subsampled data, in: Imaging, Vision and Learning Based on Optimization and PDEs IVLOPDE, Bergen, Norway, August 29  September 2, 2016, X.Ch. Tai, E. Bae, M. Lysaker, eds., Mathematics and Visualization, Springer International Publishing, Berlin, 2018, pp. Part 1, Chapter 1, 23 pages, DOI 10.1007/9783319912745 .
Abstract
Choices of regularization parameters are central to variational methods for image restoration. In this paper, a spatially adaptive (or distributed) regularization scheme is developed based on localized residuals, which properly balances the regularization weight between regions containing image details and homogeneous regions. Surrogate iterative methods are employed to handle given subsampled data in transformed domains, such as Fourier or wavelet data. In this respect, this work extends the spatially variant regularization technique previously established in [15], which depends on the fact that the given data are degraded images only. Numerical experiments for the reconstruction from partial Fourier data and for wavelet inpainting prove the efficiency of the newly proposed approach.
Preprints, Reports, Technical Reports

L. Calatroni, K. Papafitsoros, Analysis and optimisation of a variational model for mixed Gaussian and Salt & Pepper noise removal, Preprint no. 2542, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2542 .
Abstract, PDF (946 kByte)
We analyse a variational regularisation problem for mixed noise removal that was recently proposed in [14]. The data discrepancy term of the model combines L^{1} and L^{2} terms in an infimal convolution fashion and it is appropriate for the joint removal of Gaussian and Salt & Pepper noise. In this work we perform a finer analysis of the model which emphasises on the balancing effect of the two parameters appearing in the discrepancy term. Namely, we study the asymptotic behaviour of the model for large and small values of these parameters and we compare it to the corresponding variational models with L^{1} and L^{2} data fidelity. Furthermore, we compute exact solutions for simple data functions taking the total variation as regulariser. Using these theoretical results, we then analytically study a bilevel optimisation strategy for automatically selecting the parameters of the model by means of a training set. Finally, we report some numerical results on the selection of the optimal noise model via such strategy which confirm the validity of our analysis and the use of popular data models in the case of "blind” model selection. 
S. Hajian, M. Hintermüller, C. Schillings, N. Strogies, A Bayesian approach to parameter identification in gas networks, Preprint no. 2537, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2537 .
Abstract, PDF (505 kByte)
The inverse problem of identifying the friction coefficient in an isothermal semilinear Euler system is considered. Adopting a Bayesian approach, the goal is to identify the distribution of the quantity of interest based on a finite number of noisy measurements of the pressure at the boundaries of the domain. First wellposedness of the underlying nonlinear PDE system is shown using semigroup theory, and then Lipschitz continuity of the solution operator with respect to the friction coefficient is established. Based on the Lipschitz property, wellposedness of the resulting Bayesian inverse problem for the identification of the friction coefficient is inferred. Numerical tests for scalar and distributed parameters are performed to validate the theoretical results. 
G. Dong, M. Hintermüller, K. Papafitsoros, A physically oriented method for quantitative magnetic resonance imaging, Preprint no. 2528, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2528 .
Abstract, PDF (2678 kByte)
Quantitative magnetic resonance imaging (qMRI) denotes the task of estimating the values of magnetic and tissue parameters, e.g., relaxation times T_{1}, T_{2}, proton density ρ and others. Recently in [Ma et al., Nature, 2013], an approach named Magnetic Resonance Fingerprinting (MRF) was introduced, being capable of simultaneously recovering these parameters by using a two step procedure: (i) a series of magnetization maps are created and then (ii) these are matched to parameters with the help of a precomputed dictionary (Bloch manifold). In this paper, we initially put MRF and its variants in the perspective of optimization and inverse problems, providing some mathematical insights into these methods. Motivated by the fact that the Bloch manifold is nonconvex, and the accuracy of the MRF type algorithms is limited by the discretization size of the dictionary, we propose here a novel physically oriented method for qMRI. In contrast to the conventional two step models, our model is dictionaryfree and it is described by a single nonlinear equation, governed by an operator for which we prove differentiability and other properties. This nonlinear equation is efficiently solved via robust Newton type methods. The effectiveness of our method for noisy and undersampled data is shown both analytically and via numerical examples where also improvement over MRF and its variants is observed. 
J. Polzehl, K. Papafitsoros, K. Tabelow, Patchwise adaptive weights smoothing, Preprint no. 2520, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2520 .
Abstract, PDF (28 MByte)
Image reconstruction from noisy data has a long history of methodological development and is based on a variety of ideas. In this paper we introduce a new method called patchwise adaptive smoothing, that extends the PropagationSeparation approach by using comparisons of local patches of image intensities to define local adaptive weighting schemes for an improved balance of reduced variability and bias in the reconstruction result. We present the implementation of the new method in an R package aws and demonstrate its properties on a number of examples in comparison with other stateofthe art image reconstruction methods. 
A. Alphonse, M. Hintermüller, C.N. Rautenberg, Recent trends and views on elliptic quasivariational inequalities, Preprint no. 2518, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2518 .
Abstract, PDF (452 kByte)
We consider stateoftheart methods, theoretical limitations, and open problems in elliptic QuasiVariational Inequalities (QVIs). This involves the development of solution algorithms in function space, existence theory, and the study of optimization problems with QVI constraints. We address the range of applicability and theoretical limitations of fixed point and other popular solution algorithms, also based on the nature of the constraint, e.g., obstacle and gradienttype. For optimization problems with QVI constraints, we study novel formulations that capture the multivalued nature of the solution mapping to the QVI, and generalized differentiability concepts appropriate for such problems. 
H. Antil, C.N. Rautenberg, Sobolev spaces with nonMuckenhoupt weights, fractional elliptic operators, and applications, Preprint no. 2505, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2505 .
Abstract, PDF (7959 kByte)
We propose a new variational model in weighted Sobolev spaces with nonstandard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply. For special cases of the weights, the resulting variational problem is known to be equivalent to the fractional Poisson problem. The trace space for the weighted Sobolev space is identified to be embedded in a weighted L2 space. We propose a finite element scheme to solve the EulerLagrange equations, and for the image denoising application we propose an algorithm to identify the unknown weights. The approach is illustrated on several test problems and it yields better results when compared to the existing total variation techniques. 
L. Adam, M. Hintermüller, D. Peschka, Th.M. Surowiec, Optimization of a multiphysics problem in semiconductor laser design, Preprint no. 2500, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2500 .
Abstract, PDF (1472 kByte)
A multimaterial topology optimization framework is suggested for the simultaneous optimization of mechanical and optical properties to be used in the development of optoelectronic devices. Based on the physical aspects of the underlying device, a nonlinear multiphysics model for the elastic and optical properties is proposed. Rigorous proofs are provided for the sensitivity of the fundamental mode of the device with respect to the changes in the underlying topology. After proving existence and optimality results, numerical experiments leading to an optimal material distribution for maximizing the strain in a GeonSi microbridge are given. The highly favorable electronic properties of this design are demonstrated by steadystate simulations of the corresponding van Roosbroeck (driftdiffusion) system. 
A. Alphonse, M. Hintermüller, C.N. Rautenberg, Directional differentiability for elliptic quasivariational inequalities of obstacle type, Preprint no. 2492, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2492 .
Abstract, PDF (830 kByte)
The directional differentiability of the solution map of obstacle type quasivariational inequal ities (QVIs) with respect to perturbations on the forcing term is studied. The classical result of Mignot is then extended to the quasivariational case under assumptions that allow multiple solu tions of the QVI. The proof involves selection procedures for the solution set and represents the directional derivative as the limit of a monotonic sequence of directional derivatives associated to specific variational inequalities. Additionally, estimates on the coincidence set and several sim plifications under higher regularity are studied. The theory is illustrated by a detailed study of an application to thermoforming comprising of modelling, analysis and some numerical experiments.
Talks, Poster

A. Alphonse, Directional differentiability for elliptic quasivariational inequalities, Surface, Bulk, and Geometric Partial Differential Equations: Interfacial, stochastic, nonlocal and discrete structures, January 20  26, 2019, Mathematisches Forschungsinstitut Oberwolfach, January 25, 2019.

C.N. Rautenberg, Parabolic quasivariational inequalities with gradient and obstacle type constraints, Modern Maximal Monotone Operator Theory: From Nonsmooth Optimization to Differential Inclusions, January 28  February 1, 2019, Erwin Schrödinger International Institute for Mathematics and Physics (ESI), Wien, Austria, January 31, 2019.

J.A. Brüggemann, Pathfollowing methods for a class of elliptic obstacletype quasivariational problems with integral constraints, 23rd International Symposium on Mathematical Programming (ISMP2018), Session 370 ``Variational Analysis 4'', July 1  6, 2018, Bordeaux, France, July 2, 2018.

A. Alphonse, Optimal Control of Elliptic and Parabolic QuasiVariational Inequalities, Annual Meeting of the DFG Priority Programme 1962, October 1  3, 2018, Kremmen (Sommerfeld), October 3, 2018.

A. Alphonse, Parabolic quasivariational inequalities: existence and sensitivity analysis, 4th Central European SetValued and Variational Analysis Meeting (CESVVAM 2018), November 24, 2018, PhilippsUniversität Marburg, November 24, 2018.

A. Alphonse, Directional differentiability for elliptic QVIs of obstacle type, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19  23, 2018, Technische Universität München, March 20, 2018.

A. Alphonse, Directional differentiability for elliptic QVIs of obstacle type, Joint Research Seminar on Mathematical Optimization / Nonsmooth Variational Problems and Operator Equations, WIAS, May 23, 2018.

A. Alphonse, Directional differentiability for elliptic quasivariational inequalities, Workshop ``Challenges in Optimal Control of Nonlinear PDESystems'', April 8  14, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 12, 2018.

T. Keil, Simulation and Control of a Nonsmooth CahnHilliardNavierStokes System with Variable Fluid Densities, Annual Meeting of the DFG Priority Programme 1962, October 1  3, 2018, Kremmen (Sommerfeld), Germany, October 2, 2018.

T. Keil, Strong stationarity conditions for the optimal control of a CahnHilliardNavierStokes system, 5th European Conference on Computational Optimization, Session ``Infinite Dimensional Nonsmooth Optimization'', September 10  12, 2018, Trier, September 12, 2018.

S.M. Stengl, Generalized Nash equilibrium problems with partial differential operators: theory, algorithms and risk aversion, Annual Meeting of the DFG Priority Programme 1962, October 1  3, 2018, Kremmen (Sommerfeld), October 1, 2018.

S.M. Stengl, Uncertainty quantification of the AmbrosioTortorelli approximation in image segmentation, MIA 2018  Mathematics and Image Analysis, HumboldtUniversität zu Berlin, January 15  17, 2018.

C. Löbhard, Analysis, algorithms and applications for the optimal control of variational inequalities, European Women in Mathematics, General Meeting 2018, MiniSymposium 9 ``Nonsmooth PDEconstrained Optimization: Problems and Methods'', September 3  7, 2018, Graz, Austria, September 7, 2018.

C. Löbhard, Optimal shape design of air ducts in combustion engines, ROMSOC MidTerm Meeting, November 26  27, 2018, Universität Bremen, November 26, 2018.

M. Hintermüller, M. Holler, K. Papafitsoros, A function space framework for structural total variation regularization in inverse problems, MIA 2018  Mathematics and Image Analysis, HumboldtUniversität zu Berlin, January 15  17, 2018.

M. Hintermüller, Automated regularization parameter choice rule in image processing, Workshop ``New Directions in Stochastic Optimisation'', August 19  25, 2018, Mathematisches Forschungsinstitut Oberwolfach, August 23, 2018.

M. Hintermüller, Bilevel optimisation in automated regularisation parameter selection in image processing, WIASPGMO Workshop on Nonsmooth and Stochastic Optimization, June 26, 2018, HumboldtUniversität zu Berlin, June 26, 2018.

M. Hintermüller, Bilevel optimization and some "parameter learning" applications in image processing, SIAM Conference on Imaging Science, Minisymposium MS5 ``Learning and Adaptive Approaches in Image Processing'', June 5  8, 2018, Bologna, Italy, June 5, 2018.

M. Hintermüller, Generalised Nash equilibrium problems with partial differential equations, Search Based Model Engineering Workshop, August 7  9, 2018, King's College London, UK, August 7, 2018.

M. Hintermüller, Multiobjective optimization with PDE constraints, International Workshop on PDEConstrained Optimization, Optimal Controls and Applications, December 10  14, 2018, Sanya, China, December 13, 2018.

M. Hintermüller, Multiobjective optimization with PDE constraints, 23rd International Symposium on Mathematical Programming (ISMP2018), July 1  6, 2018, Bordeaux, France, July 2, 2018.

M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Mathematisches Kolloquium, Universität Bielefeld, Fakultät für Mathematik, June 7, 2017.

M. Hintermüller, Recent advances in nonsmooth and complementaritybased distributed parameter systems, 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2018), Session PP07 ``DFG Priority Program 1962'', March 19  23, 2018, Technische Universität München, March 20, 2018.

M. Hintermüller, Semismooth Newton methods in PDE constrained optimization, Advanced Training in Mathematics Schools ``New Directions in PDE Constrained Optimisation'', March 12  16, 2018, National Centre for Mathematics of IIT Bombay and TIFR, Mumbai, Bombay, India.

M. Hintermüller, Structural total variation regularization with applications in inverse problems, International Conference on Scientific Computing, December 5  8, 2018, Department of Mathematics, The Chinese University of Hong Kong, China, December 8, 2018.

K. Papafitsoros, A function space framework for structural total variation regularization with applications in inverse problems, SIAM Conference on Imaging Science, Minisymposium MS38 ``Geometrydriven Anisotropic Approaches for Imaging Problems'', June 5  8, 2018, Bologna, Italy, June 6, 2018.

K. Papafitsoros, A function space framework for structural total variation regularization with applications in inverse problems, LAWOC 2018, VI Latin American Workshop on Optimization and Control, September 3  7, 2018, Quito, Ecuador, September 4, 2018.

C.N. Rautenberg, Dissipative and nondissipative evolutionary quasivariational inequalities with derivative constraints, Joint Meeting of the Italian Mathematical Union, the Italian Society of Industrial and Applied Mathematics and the Polish Mathematical Society, Session 14 ``Nonlinear Variational Methods with Applications'', September 17  20, 2018, Wroclaw, Poland, September 19, 2018.

C.N. Rautenberg, On the optimal control of quasivariational inequalities, 23rd International Symposium on Mathematical Programming (ISMP2018), Session 221 ``Optimization Methods for PDE Constrained Problems'', July 1  6, 2018, Bordeaux, France, July 3, 2018.

C.N. Rautenberg, Optimization problems with quasivariational inequality constraints, Workshop ``Challenges in Optimal Control of Nonlinear PDESystems'', April 8  14, 2018, Mathematisches Forschungsinstitut Oberwolfach, April 11, 2018.

C.N. Rautenberg, Spatially distributed parameter selection in Total Variation (TV) models, MIA 2018  Mathematics and Image Analysis, HumboldtUniversität zu Berlin, January 15  17, 2018.

C.N. Rautenberg, Evolutionary quasivariational inequalities: Applications, theory, and numerics, 5th International Conference on Applied Mathematics, Design and Control: Mathematical Methods and Modeling in Engineering and Life Sciences, November 7  9, 2018, San Martin National University, Buenos Aires, Argentina, November 9, 2018.
Research Groups
 Partial Differential Equations
 Laser Dynamics
 Numerical Mathematics and Scientific Computing
 Nonlinear Optimization and Inverse Problems
 Interacting Random Systems
 Stochastic Algorithms and Nonparametric Statistics
 Thermodynamic Modeling and Analysis of Phase Transitions
 Nonsmooth Variational Problems and Operator Equations