Zusammenfassung für den Vortrag am 27.04.2018 (11:00 Uhr)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Luca Scarpa (University College London)
Well-posedness of semilinear SPDEs with singular drift: a variational approach
We prove well-posedness for singular semilinear SPDEs on a smooth bounded domain D in ℝn of the form <center class="math-display"> <img src="/fileadmin/lecture_img/tex_23871c0x.png" alt="dX (t)+ AX (t)dt+ β(X(t))dt ∋ B (t,X (t))dW (t), X(0) = X0. " class="math-display"></center>
The linear part is associated to a linear coercive maximal monotone operator A on L2(D), while β is 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 B taking values in the Hilbert-Schmidt operators from U to L2(D): classical Lipschitz-continuity hypotheses for the diﬀusion coeﬃcient are assumed. A comparison with the corresponding deterministic equation and possible generalizations are discussed. This study is based on a joint work with Carlo Marinelli (University College London).