Martedì 7 Novembre 2017, alle ore 15 precise, presso la sala conferenze dell’IMATI-CNR di Pavia, il

dott. Luca Scarpa, University College London

terrà un seminario dal titolo:

Well-posedness of semilinear SPDEs with singular drift: a variational approach

nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia),

Al termine della conferenza sarà organizzato un piccolo rinfresco.



Well-posedness is proved for singular semilinear SPDEs of the form
B(t, Xt) dWt ∈ dXt + AXt dt + β(Xt) dt in (0, T) × D,
X(0) = X0 in D,
where D ⊆ Rn is a smooth bounded domain, T > 0, A is a linear coercive maximal monotone operator in L2(D) and β is a maximal monotone graph everywhere defined on R, on which no growth nor smoothness conditions are required. Moreover, W is a cylindrical Wiener process on a suitable Hilbert space U, B takes values in the Hilbert-Schmidt operators from U to L2(D) and satisfies classical Lipschitz continuity hypotheses in the second variable. 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).