A Gradient Bound for Free Boundary Graphs

作者:De Silva Daniela*; Jerison David
来源:Communications on Pure and Applied Mathematics, 2011, 64(4): 538-555.
DOI:10.1002/cpa.20354

摘要

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.

  • 出版日期2011-4