English

High-Order regularity for fully nonlinear elliptic transmission problems under weak convexity assumption

Analysis of PDEs 2024-04-26 v1

Abstract

This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first scenario, it is considered that F enjoys a small ellipticity aperture. In our second case, we study regularity results where the convexity of the superlevel (or sublevel) sets is verified, implying that the operator F is quasiconcave (or quasiconvex).

Keywords

Cite

@article{arxiv.2404.16602,
  title  = {High-Order regularity for fully nonlinear elliptic transmission problems under weak convexity assumption},
  author = {G. C. Ricarte and C. S. Barroso and L. S. Tavares},
  journal= {arXiv preprint arXiv:2404.16602},
  year   = {2024}
}
R2 v1 2026-06-28T16:06:18.633Z