Geodesic
A Probabilistic Approach to Gradient Estimates
Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 46-55

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Suppose u is a harmonic function on a domain D and x, x' are in D. We estimate |u(x) — u(x')| using two Brownian motions started at x and x' and killed on exiting a cube Q ⊂ D. By selecting appropriate versions of the two Brownian motions, a classical gradient estimate for u is easily derived.
DOI : 10.4153/CMB-1992-007-6
Mots-clés : 60J45. 
Cranston, M. A Probabilistic Approach to Gradient Estimates. Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 46-55. doi: 10.4153/CMB-1992-007-6
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