Seminario di Analisi Matematica a.a. 2020/2021
15/03/2021 |
Luca Rossi - https://meet.google.com/nie-attq-ged The symmetry of solutions of elliptic equations is a classical and challenging problem in PDE, connected with stability. for solutions which are initially non-symmetric. |
Università di Roma Sapienza |
29/03/2021 |
Piermarco Cannarsa - https://meet.google.com/nie-attq-ged Sub-Riemannian systems are an important class of nonlinear control systems with linear dependence on controls. Controllability properties for such systems are derived by the so-called Lie Algebra rank condition on the associated family of vector fields. We will discuss the long-time average behaviour of the value function of optimal control problems for sub-Riemannian systems, which cannot be addressed by classical weak KAM theory as the Hamiltonian fails to be coercive in the momentum variable. |
Università di Roma Tor Vergata |
26/04/2021 |
Alessandro Carlotto - https://meet.google.com/nie-attq-ged Besides their self-evident geometric significance, which can be traced back at least to Courant, free boundary minimal surfaces also naturally arise in partitioning problems for convex bodies, in capillarity problems for fluids and, as has significantly emerged in recent years thanks to work of Fraser and Schoen, in connection to extremal metrics for Steklov eigenvalues for manifolds with boundary (i. e. for eigenvalues of the corresponding Dirichlet-to-Neumann map). |
ETH, Zürich |
10/05/2021 |
Annika Bach - https://meet.google.com/nie-attq-ged In this talk we introduce a general class of singularly-perturbed elliptic functionals Fε and we study their asymptotic behaviour as the perturbation parameter ε > 0 vanishes. Under suitable assumptions, which in particular allow us to bound Fε by the Ambrosio-Tortorelli functionals, we show that the functionals Fε Γ-converge (up to subsequences) to a free-discontinuity functional of brittle type. Moreover, we provide asymptotic formulas for the limiting volume and surface integrands, which show that the volume and surface contributions of Fε decouple in the limit. If time permits, we will discuss the application of the general convergence result to the setting of stochastic homogenisation. This is joint work with R. Marziani and C. I. Zeppieri (Münster). |
Università di Roma Sapienza |
07/06/2021 |
Pieralberto Sicbaldi - https://meet.google.com/nie-attq-ged We consider the problem of finding domains that minimize the first eigenvalue of the Dirichlet Laplacian in a Riemannian manifold under volume constraint (Faber-Krahn minimizers). In the Euclidean setting such domains are balls, and existence and regularity of such domains is trivial. In a non-Euclidean setting very few examples are known. In this talk we will show a general result of existence and regularity of Faber-Krahn minimizers, inspired by the analogous result of existence and regularity of the solutions of the isoperimetric problems in a Riemannian manifold. In particular we will show that Faber-Krahn minimizers are regular in low dimension, and that there |
Universidad de Granada |
21/06/2021 |
Henri Berestycki - https://meet.google.com/nie-attq-ged I report here on a series of joint works with Alessandro Zilio (Université de Paris) about systems of competing predators interacting with a single prey. We focus on the analysis of stationary states, stability issues, and the asymptotic behavior when the competition parameter becomes unbounded. Existence of solutions is obtained by a bifurcation theory type approach and the segregation analysis rests on a priori estimates and a free boundary problem. We discuss the classification of solutions by using spectral properties of the limiting system. Our results shed light on the conditions under which predators segregate into packs, on whether there is an advantage to have such hostile packs, and on comparing the various territory configurations that arise in this context. These questions lead us to nonstandard optimization problems. |
EHESS, Paris |