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- Title
Gradient estimates for some diffusion semigroups.
- Authors
Picard, Jean
- Abstract
Consider the semigroup $P_t$ of an elliptic diffusion; we describe a simple stochastic method providing gradient estimates on $P_tf$. If $N$ is a manifold endowed with a connection, the method can also be applied to the associated nonlinear semigroup $Q_t$ acting on $N$-valued maps. With a localization technique, we deduce gradient estimates for real harmonic functions or $N$-valued harmonic maps. Moreover, the results are extended to a class of hypoelliptic diffusions.
- Subjects
SEMIGROUPS (Algebra); STOCHASTIC processes; LOCALIZATION theory; HYPOELLIPTIC differential equations
- Publication
Probability Theory & Related Fields, 2002, Vol 122, Issue 4, p593
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s004400100185