Course by Giuseppe Da Prato - Surface integrals in Hilbert spaces for measures not necessarily Gaussian and applications to gradient estimates  18 - 20 May 2015

10:00 - 12:00

Organiser

Giuseppe Da Prato, Scuola Normale Superiore di Pisa

I will first present a new construction of surface integration in Hilbert spaces. Several papers have been devoted to this topics in the case of a Gaussian measure, starting from the pioneering papers by Airault-Malliavin and Fejer-De la Pradelle. The construction I shall present is simpler, in my opinion, and applies to non Gaussian measures as the invariant measures of some SPDEs as reaction-difusions and Burgers equations. The second part is devoted to some  L? gradient estimates for the solu-tions of the Dirichlet problem for the Ornstein-Uhenbeck operator in some open subset of a separable Hilbert spaces. Talks are essentially based on the papers [1]-[4] below.
References:
[1] G. Da Prato and A. Debussche, Estimate for PtD for the stochastic Burgers equation, arXiv:1412.7426, 2014.
[2] G. Da Prato, A Lunardi and L. Tubaro, Surface measures in infnite dimensions, Rend. Lincei Math. Appl. 25, 309{330, 2014.
[3] G. Da Prato, A Lunardi and L. Tubaro, Surface integrals in Hilbert spaces for measures not necessarily Gaussian, in preparation.
[4] G. Da Prato, A Lunardi and L. Tubaro, A new method for fi nding gradient estimates of solutions of Ornstein-Uhlenbeck equations with Dirichlet boundary conditions, in progress.

Name University Dates of visit
Giuseppe Da Prato Scuola Normale Superiore di Pisa 18/05/2015 - 20/05/2015
Total Guests : 1
Name University Dates of visit
Total Guests : 0