*Accepted Paper*

**Inserted:** 29 apr 2010

**Journal:** Advances in Mathematics

**Year:** 2009

**Abstract:**

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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