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