SEMINARIO DI MATEMATICA Venerdì 22 giugno 2018 ore 11:00 *Scuola Normale Superiore* Pisa Aula Mancini *Enrico Priola* *(Università di Torino)* terrà un seminario dal titolo: *“**Poisson stochastic process and basic parabolic estimates**”* *Abstract:* We show how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to other types of estimates and to equations involving non-local operators. It looks like no other methods are available at this time and it is a challenging problem to find an analytic approach to prove such results. In the talk I will concentrate on basic Sobolev estimates for the heat equation trying to explain the method. This is a joint work with N. V. Krylov. Tutti gli interessati sono invitati a partecipare. Classe di Scienze Valeria Giuliani Scuola Normale Superiore Servizio alla Didattica e Allievi tel. 050 509260 Piazza dei Cavalieri, 7 56126 Pisa E-mail: valeria.giuliani@sns.it E-mail: classi@sns.it