On a class of stochastic semilinear PDE's

Luigi Manca

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On a class of stochastic semilinear PDE's

Luigi Manca

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Abstract

We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space $L^2(H;ν)$, where $ν$ is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under boundness conditions on the nonlinear term, we prove a Poincaré inequality, a logarithmic Sobolev inequality and the ipercontractivity of the transition semigroup.

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BibTeX RIS

Luigi Manca. 2005-09-20. On a class of stochastic semilinear PDE's. https://arxiv.org/abs/math/0509446

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