$L^p$-$L^q$ estimates for transition semigroups associated to dissipative stochastic systems
Probability
2024-05-30 v2 Analysis of PDEs
Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2311.04523,
title = {$L^p$-$L^q$ estimates for transition semigroups associated to dissipative stochastic systems},
author = {Luciana Angiuli and Davide A. Bignamini and Simone Ferrari},
journal= {arXiv preprint arXiv:2311.04523},
year = {2024}
}