We establish partial smoothing properties of the transition semigroup (Pt) associated to the linear stochastic wave equation driven by a cylindrical Wiener noise on a separable Hilbert space. These new results allow the study of related vector-valued infinite-dimensional PDEs in spaces of functions which are Hölder continuous along special directions. As an application we prove strong uniqueness for semilinear stochastic wave equations involving nonlinearities of Hölder type. We stress that we are able to prove well-posedness although the Markov semigroup (Pt) is not strong Feller.

Masiero, F., Priola, E. (2024). Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena. JOURNAL OF THEORETICAL PROBABILITY, 37(3), 2738-2774 [10.1007/s10959-024-01337-1].

Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena

Masiero F.
;
2024

Abstract

We establish partial smoothing properties of the transition semigroup (Pt) associated to the linear stochastic wave equation driven by a cylindrical Wiener noise on a separable Hilbert space. These new results allow the study of related vector-valued infinite-dimensional PDEs in spaces of functions which are Hölder continuous along special directions. As an application we prove strong uniqueness for semilinear stochastic wave equations involving nonlinearities of Hölder type. We stress that we are able to prove well-posedness although the Markov semigroup (Pt) is not strong Feller.
Articolo in rivista - Articolo scientifico
35R60; 60H15; 60H50; Partial smoothing; Regularization by noise for semilinear stochastic equations; Stochastic wave equation; Transition semigroups;
English
20-mag-2024
2024
37
3
2738
2774
open
Masiero, F., Priola, E. (2024). Partial Smoothing of the Stochastic Wave Equation and Regularization by Noise Phenomena. JOURNAL OF THEORETICAL PROBABILITY, 37(3), 2738-2774 [10.1007/s10959-024-01337-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/501040
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