We prove a pointwise gradient bound for bounded solutions of Δu+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.
A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature / A. Farina, E. Valdinoci. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 225:5(2010), pp. 2808-2827.
A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature
E. Valdinoci
2010
Abstract
We prove a pointwise gradient bound for bounded solutions of Δu+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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