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arXiv · 2505.16757

Regularity of two-phase free boundary minimizers in periodic media

Farhan Abedin·William M Feldman
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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.

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Farhan Abedin, William M Feldman. 2025-05-22. Regularity of two-phase free boundary minimizers in periodic media. https://arxiv.org/abs/2505.16757

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