A fully nonlinear free transmission problem
Analysis of PDEs
2020-11-30 v2
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 , 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.
Cite
@article{arxiv.2010.15910,
title = {A fully nonlinear free transmission problem},
author = {Edgard A. Pimentel and Makson S. Santos},
journal= {arXiv preprint arXiv:2010.15910},
year = {2020}
}