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A Gradient Bound for Free Boundary Graphs
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DOI：10.1002/cpa.20354.png)
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Abstract
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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. (C) 2010 Wiley Periodicals, Inc.
Keywords:
REGULARITY
INEQUALITY
EXISTENCE
EQUATIONS
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