English

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 C1,1C ^{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.

Keywords

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}
}
R2 v1 2026-06-23T19:45:38.097Z