Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆
By Wei David Liu, Feng-Yu Wang. 2007
65 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/c6478722724d8fc3451745a19c03b7456c7b1afe
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In Applied Mathematics
- Wei Liu
- Michael Röckner
- Feng-Yu Wang
- Tusheng Zhang
- Shijie Shang
- Xicheng Zhang
- Giuseppe Da Prato
- Franco Flandoli
In Computational Theory and Mathematics
- Wei Liu
- Michael Röckner
- Xicheng Zhang
- Tusheng Zhang
- Wei David Liu
- Feng-Yu Wang
- Giuseppe Da Prato
- Vladimir Bogachev
Citations in the corpus
- Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, methodology): “Hence we can obtain the uniqueness of invariant measures for the transition semigroups without assuming the strict monotonicity of the drift, which has been required in many earlier works [26, 36, 20, 27, 8].”
- SPDE in Hilbert space with locally monotone coefficients (2010, methodology): “see [8, 19, 28, 32] for the small noise large deviation principle, [13, 14] for discretization approximation schemes to the solutions of SPDE, [34, 17, 18] for the dimension-free Harnack inequality and resulting ergodicity, compactness and contractivity properties of the associated transition semigr”