Martedi' 14 Novembre, ore 14, Aula di Consiglio. Titolo: Well-posedness of semilinear SPDEs with singular drift: a variational approach
Speaker: Luca Scarpa ( Department of Mathematics University College London, UK)
Abstract. Well-posedness is proved for singular semilinear SPDEs on a smooth bounded domain D in R^n. The linear part is associated to a coercive linear maximal monotone operator on L^2(D) while the drift is represented by a multivalued maximal monotone graph everywhere defined on R, on which no growth nor smoothness conditions are required. Moreover, the noise is given by a cylindrical Wiener process on a Hilbert space U, with a stochastic integrand taking values in the Hilbert-Schmidt operators from U to L^2(D): classical Lipschitz-continuity hypotheses for the diffusion coefficient are assumed. The proof consists in approximating the equation, finding uniform estimates both pathwise and in expectation on the approximated solutions, and then passing to the limit using compactness and lower semicontinuity results. Finally, possible generalizations are discussed. This study is based on a joint work with Carlo Marinelli (University College London).