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

Federica Masiero () and Enrico Priola ()
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Federica Masiero: Università di Milano-Bicocca
Enrico Priola: Università di Pavia

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 2738-2774

Abstract: Abstract We establish partial smoothing properties of the transition semigroup $$(P_t)$$ ( P t ) 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 $$(P_t)$$ ( P t ) is not strong Feller.

Keywords: Partial smoothing; Transition semigroups; Stochastic wave equation; Regularization by noise for semilinear stochastic equations; 60H15; 60H50; 35R60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01337-1

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