Harnack Inequality and Applications for Stochastic Evolution Equations with Monotone Drifts
arXiv:0802.0289 · doi:10.1007/s00028-009-0032-8
Abstract
In this paper, the dimension-free Harnack inequality is proved for the associated transition semigroups to a large class of stochastic evolution equations with monotone drifts. As applications, the ergodicity, hyper-(or ultra-)contractivity and compactness are established for the corresponding transition semigroups. Moreover, the exponential convergence of the transition semigroups to invariant measure and the existence of a spectral gap are also derived. The main results are applied to many concrete stochastic evolution equations such as stochastic reaction-diffusion equations, stochastic porous media equations and the stochastic p-Laplace equation in Hilbert space.
25 pages, to appear in J. Evol. Equ
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Cited by in corpus (10)
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- Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators
- Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts
- Ergodicity and local limits for stochastic local and nonlocal p-Laplace equations
- Distribution Dependent Stochastic Porous Media Equations
- Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises
- The stochastic Klausmeier system and a stochastic Schauder-Tychonoff type theorem
- Harnack Inequalities and Ergodicity of Stochastic Reaction-Diffusion Equation in