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arXiv · 1009.4694

A gradient bound for free boundary graphs

Daniela De Silva·David Jerison
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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.

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Daniela De Silva, David Jerison. 2010-09-23. A gradient bound for free boundary graphs. https://arxiv.org/abs/1009.4694

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