期刊
JOURNAL OF FUNCTIONAL ANALYSIS
卷 236, 期 1, 页码 244-264出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jfa.2005.12.010
关键词
gradient estimates; diffusion semigroups; coupling
类别
Uniform gradient estimates are derived for diffusion semigroups, possibly with potential, generated by second order elliptic operators having irregular and unbounded coefficients. We first consider the R-d-case, by using the coupling method. Due to the singularity of the coefficients, the coupling process we construct is not strongly Markovian, so that additional difficulties arise in the study. Then, more generally, we treat the case of a possibly unbounded smooth domain of R-d with Dirichlet boundary conditions. We stress that the resulting estimates are new even in the R-d-case and that the coefficients can be Holder continuous. Our results also imply a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying diffusion semigroup. (c) 2005 Published by Elsevier Inc.
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