Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations
arXiv:0712.3136 · doi:10.1016/j.jmaa.2007.12.047
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.
to appear in Journal of Mathematical Analysis and Applications
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