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

Luciana Angiuli; Davide A. Bignamini; Simone Ferrari

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arXiv · 2311.04523

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

Luciana Angiuli·Davide A. Bignamini·Simone Ferrari

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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.

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BibTeX RIS

Luciana Angiuli, Davide A. Bignamini, Simone Ferrari. 2023-11-08. $L^p$-$L^q$ estimates for transition semigroups associated to dissipative stochastic systems. https://arxiv.org/abs/2311.04523

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