Regularity results for interface problems in 2D
- Petzoldt, Martin
2010 Mathematics Subject Classification
- 35B65 35J25 35J20 34L15
- elliptic equations, regularity, interface problems, transmission problems, singularities, discontinuous diffusion coeffcients, Sturm-Liouville eigenvalue problem
We investigate the regularity of solutions of interface problems in 2D. Our objective are regularity results which are independent of global bounds of the data (the diffusion). Therefore we introduce a criterion on the data,the quasi-monotonicity condition, which we show to be sufficient and necessary to provide regularity better then H1. In the proof we use estimates of eigenvalues of a related Sturm-Liouville eigenvalue problem. This approach allows to derive sharp regularity results for quite a large class of configurations. Additionally we give a regularity result depending on the global bounds of the data.