Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator
Analysis of PDEs
2025-07-01 v2
Abstract
We show that any minimizer of the well-known ACF functional (for the -Laplacian) is a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, that boils down to regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument.
Cite
@article{arxiv.2301.11775,
title = {Regularity in the two-phase Bernoulli problem for the $p$-Laplace operator},
author = {Masoud Bayrami-Aminlouee and Morteza Fotouhi},
journal= {arXiv preprint arXiv:2301.11775},
year = {2025}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1911.02165 by other authors