SEMINARI DI CALCOLO DELLE VARIAZIONI

Liouville-type problems on compact surfaces: a variational approach

Abstract. A class of Liouville equations and systems on compact surfaces is considered: we focus on the Toda system which is motivated in mathematical physics by the study of models in non-abelian Chern-Simons theory and in geometry in the description of holomorphic curves. We discuss its variational aspects which yield existence results.
Data Seminario: 
Wednesday, October 25, 2017
Relatore: 
Aleks Jevnikar
Ora Fine: 
0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 17:00

The quantum conditional Entropy Power Inequality

Relatore: 
Giacomo De Palma
Abstract. The Entropy Power Inequality states that the Shannon differential entropy of the convolution of two probability densities in R^n with given entropies is minimum when they are both Gaussian. This functional inequality is fundamental in information theory and was conjectured by C. Shannon himself, although he only proved that Gaussian densities are critical points; a full proof was later given by A. Stam, using an interpolation argument along the heat semigroup.
Data Seminario: 
Tuesday, September 19, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
QMATH, University of Copenhagen
Ora Inizio: 
0000 - 17:00

An exact self-similar solution to a branched transport problem

Relatore: 
Michael Goldman
Abstract. In this talk I will show how one can exactly compute the minimizer of a variant of branched transportation arising as a simplified model for pattern formation in type-I superconductors. The proof relies on the natural scaling properties of the problem. A 3D version of this model has recently been derived from the full Ginzburg-Landau model together with S. Conti, S. Serfaty and F. Otto.
Data Seminario: 
Wednesday, May 31, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
CNRS, Laboratoire Jacques-Louis Lions
Ora Inizio: 
0000 - 17:00

A variational approach to nonlocal curvature motions and to the crystalline mean curvature flow

Relatore: 
Massimiliano Morini
Abstract. In the first part of the talk I will present a comprehensive theory that covers in a unified way a rather large class of (possibly) nonlocal geometric flows bearing a gradient flow structure with respect to suitable generalized perimeters. Within this framework one can establish new existence and uniqueness results as well as recover several examples scattered in the literature. In the second part I will discuss a new distributional formulation that allows one to treat the highly "degenerate" case of crystalline
Data Seminario: 
Wednesday, May 17, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Universita' di Parma
Ora Inizio: 
0000 - 17:00

On the quantitative Bossel-Daners Inequality

Relatore: 
Cristina Trombetti
Abstract. The Bossel-Daners is a Faber-Krahn type inequality for the first Laplacian eigenvalue with Robin boundary conditions. We prove a stability result for such inequality.
Data Seminario: 
Wednesday, May 10, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Universita' di Napoli Federico II
Ora Inizio: 
0000 - 17:00

Optimizing the fractional power of a Diffusion operator

Abstract. We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter $s$ is the $s$-th power of the diffusion operator in the state equation. Before moving to the SPDE case, we first describe the result of Sprekels-Valdinoci for the PDE case. Then we discuss a suitable concept of solutions of the state equation and establish pathwise differentiability properties of the stochastic process w.r.t. the fractional parameter $s$. Finally, we show that under certain conditions on the noise, optimality conditions for
Data Seminario: 
Wednesday, April 26, 2017
Relatore: 
Carina Geldhauser
Ora Fine: 
0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 17:00

Scalar conservation laws with discontinuous flux

Relatore: 
Francesco Ghiraldin
Abstract. In the talk I will investigate the uniqueness of solutions of scalar conservation laws with discontinuous flux. While in the smooth setting this property follows from Kruzhkov's entropy inequalities, in the case of discontinuous fluxes these inequalities are not enough and additional dissipation conditions must be imposed at the discontinuity set of the flux. I will explain how any entropy solution admits traces on the discontinuity set of the flux field and use this to prove the validity of a generalized Kato inequality for any pair of solutions.
Data Seminario: 
Wednesday, May 3, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Max Planck Institute Leipzig
Ora Inizio: 
0000 - 17:00

Numerical study of 1D optimal structures

Relatore: 
Edouard Oudet
Abstract. We focus our attention on shape optimization problems in which one dimensional connected objects are involved. Very old and classical problems in calculus of variation are of this kind: euclidean Steiner's tree problem, optimal irrigation networks, cracks propagation, etc. In a first part we quickly recall some previous work in collaboration with F. Santambrogio related to the functional relaxation of the irrigation cost. We establish a $\Gamma$-convergence of Modica and Mortola's type and illustrate its efficiency from a numerical point of
Data Seminario: 
Wednesday, April 19, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 19:00
Affiliazione: 
Université Grenoble Alpes
Ora Inizio: 
0000 - 18:00

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