Two-phase free boundary problems for a class of fully nonlinear double-divergence systems
Analysis of PDEs
2025-08-21 v2
Abstract
In this article, we study a class of fully nonlinear double-divergence systems with free boundaries associated with a minimization problem. The variational structure of Hessian-dependent functional plays a fundamental role in proving the existence of the minimizers and then the existence of the solutions for the system. In addition, we establish gains of the integrability for the double-divergence equation. Consequently, we improve the regularity for the fully nonlinear equation in Sobolev and H\"older spaces.
Cite
@article{arxiv.2305.19236,
title = {Two-phase free boundary problems for a class of fully nonlinear double-divergence systems},
author = {Pêdra D. S. Andrade and Julio C. Correa},
journal= {arXiv preprint arXiv:2305.19236},
year = {2025}
}
Comments
18 pages, 1 figure