Regularity of two-phase free boundary minimizers in periodic media
Analysis of PDEs
2025-05-23 v1
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.
Keywords
Cite
@article{arxiv.2505.16757,
title = {Regularity of two-phase free boundary minimizers in periodic media},
author = {Farhan Abedin and William M Feldman},
journal= {arXiv preprint arXiv:2505.16757},
year = {2025}
}