A gradient estimate on a manifold with convex boundary
Zhongmin Qian · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1997
We present a simple probability approach for establishing a gradient estimate for a solution of an elliptic equation on a compact Riemannian manifold with convex boundary, or on a noncompact complete manifold. Our method can also be applied to derive a similar gradient estimate for a nonlinear parabolic equation, and an abstract gradient estimate for a Markov semigroup.