Large scale regularity of almost minimizers of the one-phase problem in periodic media

TL;DR

This paper establishes large-scale regularity results for almost minimizers of one-phase free boundary problems in periodic media, showing Lipschitz continuity and flatness implications.

Contribution

It extends regularity theory to periodic media for almost minimizers, adapting techniques from homogeneous media.

Findings

Lipschitz estimates hold at large scales for almost minimizers.

Flat free boundaries imply Lipschitz regularity.

Techniques from homogeneous media are successfully adapted.

Abstract

We prove that minimizers and almost minimizers of one-phase free boundary energy functionals in periodic media satisfy large scale (1) Lipschitz estimates (2) free boundary flat implies Lipschitz estimates. The proofs are based on techniques introduced by De Silva and Savin for almost minimizers in homogeneous media.