Harnack inequality and strong Feller property for stochastic fast-diffusion equations |
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Authors: | Wei Liu Feng-Yu Wang |
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Institution: | a School of Mathematics, Beijing Normal University, Beijing 100875, China b Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, UK c Fakultät für Mathematik, Universität Bielefeld, D-33501 Bielefeld, Germany |
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Abstract: | As a continuation to F.-Y. Wang, Harnack inequality and applications for stochastic generalized porous media equations, Ann. Probab. 35 (2007) 1333-1350], where the Harnack inequality and the strong Feller property are studied for a class of stochastic generalized porous media equations, 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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Keywords: | Harnack inequality Strong Feller property Stochastic fast-diffusion equation |
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