English

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.

Keywords

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}
}
R2 v1 2026-06-21T16:18:19.231Z