Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals
Analysis of PDEs
2020-11-23 v2 Classical Analysis and ODEs
Abstract
In [David-Toro 15] and [David-Engelstein-Toro 19], (some of) the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli in [Alt-Caffarelli 81] and Alt, Caffarelli and Friedman in [Alt-Caffarelli-Friedman 84]. In this paper we study the regularity of almost minimizers to energy functionals with variable coefficients (as opposed to [DT15, DET19. AC 81] and [ACF84] which deal only with the "Laplacian" setting). We prove Lipschitz regularity up to, and across, the free boundary, generalizing the results of [David-Toro 15] to the variable coefficient setting.
Cite
@article{arxiv.1909.05043,
title = {Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals},
author = {Guy David and Max Engelstein and Mariana Smit Vega Garcia and Tatiana Toro},
journal= {arXiv preprint arXiv:1909.05043},
year = {2020}
}
Comments
41 pages. Revised version has minor corrections and additions. To appear in Math Z