A gradient bound for free boundary graphs |
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| Authors: | Daniela De Silva David Jerison |
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| Institution: | 1. Columbia University, Barnard College, Department of Mathematics, 2990 Broadway, Room 518, New York, NY 10027;2. Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Room 2‐247, Cambridge, MA 02139‐4307 |
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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. © 2010 Wiley Periodicals, Inc. |
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