Dear Colleagues,

We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi: *Stochastic obstacle problems: variational & non variational settings* by Yassine Tahraoui (Scuola Normale Superiore)

The seminar will take place tomorrow TUE, 14.05.2024 at 14:00 CET in Aula Seminari, Dipartimento di Matematica, UNIPI and streamed online at the link below.

The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass

*---------------------------------------------------------* *Abstract: Obstacle problems are free boundary type problems, well known in the literature of applied mathematics and lead to numerous applications. My aim is to present some results about the well-posedness and the regularity of the solution to a "parabolic or hyperbolic" obstacle problem in the presence of multiplicative noise, studied in [1, 2]. After showing the well-posedness of such problems, we prove Lewy-Stampacchia's inequalities, which gives an estimate of the reflected measure generated by the singularities caused by the obstacle near the free boundary.* *[1]I. H. Biswas, Y. Tahraoui and G. Vallet: Obstacle problem for a stochastic conservation law and Lewy-Stampacchia inequality. Journal of Mathematical Analysis and Applications, 527 (1) 127356 (2023)* *[2]Y. Tahraoui and G.Vallet: Lewy-Stampacchia's inequality for a stochastic T-monotone obstacle problem. Stochastic Partial Differential Equations: Analysis and Computations 10, 90-125 (2022).*