NDLI: Harnack inequality and applications for stochastic evolution equations with monotone drifts

Content Provider	Springer Nature Link
Author	Liu, Wei
Copyright Year	2009
Abstract	As a Generalization to Wang (Ann Probab 35:1333–1350, 2007) where the dimension-free Harnack inequality was established for stochastic porous media equations, this paper presents analogous results for a large class of stochastic evolution equations with general monotone drifts. Some ergodicity, compactness and contractivity properties are established for the associated transition semigroups. Moreover, the exponential convergence of the transition semigroups to invariant measure and the existence of a spectral gap are also derived. As examples, the main results are applied to many concrete SPDEs such as stochastic reaction-diffusion equations, stochastic porous media equations and the stochastic p-Laplace equation in Hilbert space.
Ending Page	770
Page Count	24
Starting Page	747
File Format	PDF
ISSN	14243199
e-ISSN	14243202
Journal	Journal of Evolution Equations
Issue Number	4
Volume Number	9
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2009-08-26
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Harnack inequality Porous media equation Stochastic evolution equation Strong Feller property Stochastic partial differential equations Spectral gap p-Laplace equation Analysis Ergodicity Transition functions, generators and resolvents Markov semigroups and applications to diffusion processes
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Harnack inequality and applications for stochastic evolution equations with monotone drifts