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arXiv · 0802.0289

Harnack Inequality and Applications for Stochastic Evolution Equations with Monotone Drifts

Wei Liu
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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.

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Wei Liu. 2009-09-10. Harnack Inequality and Applications for Stochastic Evolution Equations with Monotone Drifts. https://doi.org/10.1007/s00028-009-0032-8

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