(L^p\)-\(L^q\) estimates for transition semigroups in Hilbert spaces

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

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Angiuli, Luciana, Bignamini, Davide A, Ferrari, Simone
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.11.2023
Subjects
Hilbert space
Partial differential equations
Reaction-diffusion equations
Semigroups
Online AccessGet full text

Cover

More Information
Summary:In a separable Hilbert space, we study hypercontractivity and supercontractivity properties for a transition semigroup associated with a stochastic partial differential equation. This is done in terms of exponential integrability of Lipschitz functions and some logarithmic Sobolev-type inequalities with respect to invariant measures. The supercontractivity of the transition semigroup associated to a stochastic reaction-diffusion equation is then deduced.
ISSN:2331-8422