English

Continuity up to the boundary for minimizers of the one-phase Bernoulli problem

Analysis of PDEs 2024-08-20 v1

Abstract

We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and H\"older-continuous boundary data. As an application, we use them to extend recent generic uniqueness and regularity results to families of continuous functions.

Keywords

Cite

@article{arxiv.2408.10019,
  title  = {Continuity up to the boundary for minimizers of the one-phase Bernoulli problem},
  author = {Xavier Fernández-Real and Florian Gruen},
  journal= {arXiv preprint arXiv:2408.10019},
  year   = {2024}
}

Comments

16 pages, 1 figure