A Short Proof of Optimal Regularity for minimizers of the Alt-Phillips Problem

Kunyi; Ma

A Short Proof of Optimal Regularity for minimizers of the Alt-Phillips Problem

Analysis of PDEs 2026-07-09 v1

Authors: Kunyi , Ma

Abstract

We give a self-contained short proof of optimal regularity for minimizers of the Alt-Phillips Free Boundary Problem for $\gamma \in (0, 1)$ . We adopt a dichotomy argument that originates from [DS20].

Keywords

Alt-Phillips problem free boundary problem optimal regularity minimizers dichotomy argument

Cite

@article{arxiv.2607.08685,
  title  = {A Short Proof of Optimal Regularity for minimizers of the Alt-Phillips Problem},
  author = {Kunyi and Ma},
  journal= {arXiv preprint arXiv:2607.08685},
  year   = {2026}
}