Calculus of Variations and Geometric Measure Theory
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A. Farina - E. Valdinoci

A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature

created by farina on 29 Apr 2010


Accepted Paper

Inserted: 29 apr 2010

Journal: Advances in Mathematics
Year: 2009


We prove a pointwise gradient bound for bounded solutions of the equation $ \, \Delta u+F'(u)=0 $ in possibly unbounded proper domains whose boundary has nonnegative mean curvature.

We also obtain some rigidity results when equality in the bound holds at some point.


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