A gradient bound for free boundary graphs
Analysis of PDEs
2010-09-24 v1
Abstract
We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free boundary that is a graph is also smooth. The method we use also leads to a new proof of the classical minimal surface gradient bound.
Cite
@article{arxiv.1009.4694,
title = {A gradient bound for free boundary graphs},
author = {Daniela De Silva and David Jerison},
journal= {arXiv preprint arXiv:1009.4694},
year = {2010}
}