A gradient bound for free boundary graphs

Details A gradient bound for free boundary graphs A gradient bound for free boundary graphs

2010-09-23

arxiv.org/abs/1009.4694v1

Mathematics

Analysis of PDEs

Scientific paper

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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