Data: 11/06/2018

Ora: 14:30:00

Descrizione: ]]>

Data: 16/04/2018

Ora: 12:00:00

Descrizione:

We analyze minimal partition problems for the eigenvalues of Sturm-Liouville operators. As a byproduct, by purely variational techniques, we recover some classical results: the asymptotic distribution of the zeros of eigenfunctions, the asymptotics of the eigenvalues and the Weyl law.

]]>Data: 10/04/2018

Ora: 11:30:00

Descrizione:

In this talk, I present (the full range of) Hardy's and Caffarelli, Kohn, Nirenberg's inequalites for fractional Sobolev spaces. I also mention their improvements in the classical setting where the information of the gradient is replaced by the one of some non-local, non-convex functionals used in the approximations of BV and Sobolev norms. Interestingly, the proofs of these results are quite simple and mainly based on the Poincare and Sobolev inequalities for an annulus. Assuming these inequalities, no integration by parts is required in the proofs. This is joint work with Marco Squassina.

]]>Data: 26/03/2018

Ora: 12:00:00

Descrizione:

As well known (by third Kepler’s law) the Kepler problem has many

periodic solutions with minimal period T (for any given T > 0). We will

try to understand how many of them survive after a T-periodic external

perturbation preserving the Newtonian structure of the equation. In doing

this, we will be naturally led to the concept of generalized solution and

to the theory of regularization of collisions in Celestial Mechanics.

Joint work with Rafael Ortega (Granada) and Lei Zhao (Augsburg).

Data: 19/03/2018

Ora: 12:00:00

Descrizione:

In this seminar I will present some results on the electrostatic Born-Infeld equation set in the whole R^n.

This equation is governed by the Lorentz-Minkowski mean curvature operator and was introduced, in the theory of nonlinear electromagnetism, as a generalization of the Poisson equation for the electrostatic potential.

I will consider the case of a superposition of (possibly non-symmetrically distributed) point charges and discuss sufficient conditions to guarantee that the minimizer of the energy functional associated to the problem is a solution.

I will also present an approximation of the considered problem, governed by a sum of 2m-Laplacians, and show some qualitative properties of the approximating solutions, such as their behavior near the charges.

This is a joint work with Denis Bonheure (Université Libre de Bruxelles) and Juraj Foldes (University of Virginia) available at arXiv:1707.07517.

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