Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations

Details Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations

2007-12-19

arxiv.org/abs/0712.3136v1

Mathematics

Probability

to appear in Journal of Mathematical Analysis and Applications

Scientific paper

This paper presents analogous results for stochastic fast-diffusion equations. Since the fast-diffusion equation possesses weaker dissipativity than the porous medium one does, some technical difficulties appear in the study. As a compensation to the weaker dissipativity condition, a Sobolev-Nash inequality is assumed for the underlying self-adjoint operator in applications. Some concrete examples are constructed to illustrate the main results.

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