A Gradient Bound for Free Boundary Graphs
Author(s)De Silva, Daniela; Jerison, David S.
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications on Pure and Applied Mathematics
Wiley Blackwell (John Wiley & Sons)
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.
Author's final manuscript