Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals

2019/09/11 by David, Guy, Engelstein, Max, Garcia, Mariana Smit Vega +1 · 1 citation
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.05043

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.

Cited by

• Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth

Related

• Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
• Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth
• Lipschitz regularity of a weakly coupled vectorial almost-minimizers for the p-Laplacian
• Regularity for almost minimizers with free boundary
• Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces