Antonio Segatti, Università degli studi di Pavia, A gradient flow approach to a porous medium equation with fractional pressure, Wednesday, June 14, 2017, time 14:15, Aula seminari 3° piano
Abstract:Abstract:
In this seminar I will show how a porous medium equation with fractional pressure, that has been recently introduced and studied by Caffarelli and Vazquez,can be understood as a Wasserstein gradient flow. The results include the energy dissipation inequality, the regularizing effect and decay estimates for the L^p norms. This is a joint work with S. Lisini and E. Mainini. dimat.unipv.it/segatti

Enrico Laeng, Politecnico di Milano, A quantitative Riemann-Lebesgue Lemma with application to equations with memory, Wednesday, June 14, 2017, time 16:00, Aula seminari 3° piano
Abstract:Abstract:
We prove a quantitative version of the Riemann-Lebesgue lemma for functions supported on the half-line. We apply our result to some linear differential equations with memory, obtaining optimal decay rates for solutions at infinity.

Wilfredo Urbina, Roosevelt University - Chicago USA, Transference results from the $L^p$ continuity of operators in the Jacobi case to the $L^p$ continuity of operators in the Hermite and Laguerre case, Wednesday, May 24, 2017, time 13:15, Aula seminari 3° piano
Abstract:Abstract:
Using the well known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials we develop a transference method to obtain the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the Laguerre-Riesz transform from the $L^p$-continuity of the Jacobi-Riesz transform, in dimension one as well as the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the Laguerre-Riesz transform from the $L^p$-continuity of the Jacobi-Riesz transform. The case of the corresponding Littlewood-Paley g-functions will also be discussed.

Catherine Bandle, University of Basel, Sublinear elliptic problems with a Hardy potential, Thursday, May 11, 2017, time 14:15, Aula Consiglio 7° piano
Abstract:Abstract:
We discuss the existence and the boundary behavior of positive solutions of an elliptic equation with a Hardy potential and a sublinear nonlinearity. This problem has two particular features: the Hardy potential is singular at the boundary and the unique continuation property doesn’t hold. The Hardy potential forces the solutions either to vanish or to blow up at the boundary. The picture of the radial solutions in balls and annuli is fairly complete. At the end we present results for general domains and point out some open problems.

Jean-Christophe Pesquet, University Saclay, Proximity operator computation for large scale problems, Tuesday, April 11, 2017, time 15:00 o'clock, Aula seminari 3° piano
Abstract:Abstract:
Proximal methods have gained much interest for solving large-scale possibly non smooth optimization problems. When dealing with complicated convex functions, the expression of the proximity operator is however often non explicit and it thus needs to be determined numerically. We show in this work how block-coordinate algorithms can be designed to perform this task. We deduce also distributed optimization strategies allowing us to implement our solutions on multicore architectures. Applications of these methods to video restoration of old TV sequences illustrate the good performance of the proposed algorithms.

Filippo Dell'Oro, Politecnico di Milano, Asymptotic analysis of linear Moore-Gibson-Thompson equations, Wednesday, March 29, 2017, time 15:15 o'clock, Aula seminari 3° piano
Abstract:Abstract:
We consider the linear third-order Moore-Gibson-Thompson equation arising in acoustics, together with its memory relaxation. We analyze the stability properties of the solutions in dependence of the structural parameters of the models, and we discuss some intrinsic connections with the equation of linear viscoelasticity