Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations
Probability
2015-05-13 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0712.3136,
title = {Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations},
author = {Wei Liu and Feng-Yu Wang},
journal= {arXiv preprint arXiv:0712.3136},
year = {2015}
}
Comments
to appear in Journal of Mathematical Analysis and Applications