English

$L^p$-$L^q$ 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}
}