A Gradient Bound for Free Boundary Graphs

Author(s)
De Silva, Daniela; Jerison, David S.
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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.
Date issued
2010-12
URI
http://hdl.handle.net/1721.1/71210
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Communications on Pure and Applied Mathematics
Publisher
Wiley Blackwell (John Wiley & Sons)
Citation
De Silva, Daniela, and David Jerison. “A Gradient Bound for Free Boundary Graphs.” Communications on Pure and Applied Mathematics 64.4 (2011): 538–555. Web. 26 June 2012. © 2010 Wiley Periodicals, Inc.
Version: Author's final manuscript
ISSN
0010-3640
1097-0312
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