L^p$-$L^q$ estimates for transition semigroups associated to dissipative stochastic systems

In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroups associated with a stochastic partial differential equations. This is done in terms of exponential integrability of Lipschitz functions and some logarithmic Sobolev-type inequalitie...

Full description

Saved in:
Bibliographic Details
Main Authors Angiuli, Luciana, Bignamini, Davide A, Ferrari, Simone
Format Journal Article
LanguageEnglish
Published 08.11.2023
Subjects
Mathematics - Analysis of PDEs
Mathematics - Functional Analysis
Mathematics - Probability
Online AccessGet full text

Cover

More Information
Summary:In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroups associated with a stochastic partial differential equations. This is done in terms of exponential integrability of Lipschitz functions and some logarithmic Sobolev-type inequalities with respect to invariant measures. The abstract characterization results concerning the improving of summability can be applied to transition semigroups associated to a stochastic reaction-diffusion equations.
DOI:10.48550/arxiv.2311.04523