WIAS Preprint No. 2042, (2014)
A nonlocal free boundary problem
- Dipierro, Serena
- Savin, Ovidiu
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 35R35 49Q20 49Q05
- Fractional perimeter, minimization problem, monotonicity formula, classification of cones
We consider a nonlocal free boundary problem built by a fractional Dirichlet norm plus a fractional perimeter. Among other results, we prove a monotonicity formula for the minimizers, glueing lemmata, uniform energy bounds, convergence results, a regularity theory for the planar cones and a trivialization result for the flat case. Several classical free boundary problems are limit cases of the one that we consider in this paper.
- SIAM J. Math. Anal., 47 (2015) pp. 4559--4605.