Solutions to a two-dimensional, Neumann free boundary problem
Analysis of PDEs
2017-08-31 v1
Abstract
We explore regularity properties of solutions to a two-phase elliptic free boundary problem near a Neumann fixed boundary in two dimensions. Consider a function u, which is harmonic where it is not zero and satisfies a gradient jump condition weakly along the free boundary. Our main result is that u is Lipschitz continuous up to the Neumann fixed boundary. We also present a numerical exploration of the way in which the free and fixed boundaries interact.
Cite
@article{arxiv.1708.09329,
title = {Solutions to a two-dimensional, Neumann free boundary problem},
author = {Sarah Raynor and John A. Gemmer and Gary Moon},
journal= {arXiv preprint arXiv:1708.09329},
year = {2017}
}