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arXiv · 0712.3136

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

Wei Liu·Feng-Yu Wang
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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.

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Wei Liu, Feng-Yu Wang. 2007-12-19. Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations. https://doi.org/10.1016/j.jmaa.2007.12.047

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