Regularity of two-phase free boundary minimizers in periodic media

2025/05/22 by Abedin, Farhan, Feldman, William M
#35B27 #35B65 #49Q05 #5R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.16757

Abstract

We study the regularity of minimizers of a two-phase energy functional in periodic media. Our main result is a large scale Lipschitz estimate. We also establish improvement-of-flatness for non-degenerate minimizers, which is a key ingredient in the proof of the Lipschitz estimate. As a consequence, we obtain a Liouville property for entire non-degenerate minimizers.

Related

• Large scale regularity of almost minimizers of the one-phase problem in periodic media
• Almost minimizers of the one-phase free boundary problem
• Regularity in the two-phase Bernoulli problem for the p-Laplace operator
• Regularity of the free boundary for the two-phase Bernoulli problem
• Thin One-Phase almost minimizers