A fully nonlinear free transmission problem
Abstract
We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogeneously, our analysis is two-fold: we study the regularity of the solutions and some geometric properties of the free boundary. By relating our problem with a pair of viscosity inequalities, we prove that strong solutions are of class $C ^{1,1}$, locally. As regards the free boundary, we start by establishing weak results, such as its non-degeneracy, and proceed with the characterization of global solutions.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.15910
- arXiv:
- arXiv:2010.15910
- Bibcode:
- 2020arXiv201015910P
- Keywords:
-
- Mathematics - Analysis of PDEs;
- 35B65;
- 35R35;
- 35J60