Branch Points for (Almost-)Minimizers of Two-Phase Free Boundary Problems
Analysis of PDEs
2022-04-13 v1
Abstract
We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt- Caffarelli-Friedman type functional whose free boundaries contain branch points in the strict interior of the domain. We also give an example showing that branch points in the free boundary of almost-minimizers of the same functional can have very little structure. This last example stands in contrast with recent results of De Philippis- Spolaor-Velichkov on the structure of branch points in the free boundary of stationary solutions.
Keywords
Cite
@article{arxiv.2204.05367,
title = {Branch Points for (Almost-)Minimizers of Two-Phase Free Boundary Problems},
author = {Guy David and Max Engelstein and Mariana Smit Vega Garcia and Tatiana Toro},
journal= {arXiv preprint arXiv:2204.05367},
year = {2022}
}
Comments
30 pages, 5 figures. Comments Welcome!