✦ LIBER ✦

Gradient Estimates for Harmonic Functions on Regular Domains in Riemannian Manifolds

✍ Scribed by Anton Thalmaier; Feng-Yu Wang

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 247 KB
Volume: 155
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3220

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✦ Synopsis

Derivative formulae for heat semigroups are used to give gradient estimates for harmonic functions on regular domains in Riemannian manifolds. This probabilistic method provides an alternative to coupling techniques, as introduced by Cranston, and allows us to improve some known estimates. We discuss two slightly different ways to exploit derivative formulae where each one should be interesting by itself.