Let (M, g) be a compact Riemannian manifold with boundary. In this talk I will be interested in the set of scalar-flat metrics on M which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. I will mainly…

# Categoria evento: Analysis Seminar

## A direct approach to Plateau’s problem. – Francesco Ghiraldin

I will present a direct approach to solve the the Plateau problem. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of $R^n$: the existence result is obtained by a compactness…

## “Shape optimization problems with Robin conditions on the free boundary” – Dorin Bucur (Université de Savoie, France)

Motivated by spectral optimization problems, we provide a free discontinuity approach to a class of shape optimization problems involving Robin conditions on the free boundary. More precisely, we identify a large family of domains on which such…

## “On the first nontrivial Neumann eigenvalue of the infinity Laplacian” – Carlo Nitsch (Università Federico II, Napoli)

The first nontrivial eigenfunction of the Neumann eigenvalue problem for the p-Laplacian converges, as $p$ goes to $\infty$, to a viscosity solution of a suitable eigenvalue problem for the $\infty$-Laplacian. We show among other things that the…

## Perturbations of variational evolutions – Andrea Braides (Universita’ di Roma “Tor Vergata)

The notion of minimizing movement (Almgren-Taylor-Wang, De Giorgi), which has been used to give a general definition of gradient flow (Ambrosio-Gigli-Savaré) can also be used to study a “homogenized” motion for a family of functionals depending on a…

## Lipschitz Metrics for Nonlinear Wave Equations – Alberto Bressan (Penn State University)

The talk is concerned with some classes of nonlinear wave equations: of first order, such as the Camassa-Holm equation, or of second order, as the variational wave equation $u_{tt} – c(u) (c(u)u_x)_x=0$. In both cases, it is known that the equations…

## Optimal transport with relativistic cost: continuity and Kantorovich potentials for generic cost functions – Jean Louet

The optimal transport problem consists in minimizing the total energy of the displacement among all the (vector-valued) functions having prescribed image measure. In this talk we are interested in a particular case of cost functions: c is given by…

## Discrete to continuum limits of fully atomistic and quasicontinuum systems with potentials of Lennard-Jones type – Anja Schloemerkemper

In recent years several engineering models, e.g., in the context of elasticity theory, were justified by a discrete to continuum analysis, i.e., by a passage from discrete/atomistic systems to continuum problems. I will present results with M.…

## A variational approach to nonlocal and crystalline curvature flows – Marcello Ponsiglione (Università di Roma La Sapienza)

In this seminar I will introduce a generalized notion of (local and nonlocal) perimeter and curvature. Then, I will describe the corresponding geometric flows, showing the coherence between variational methods (based on the minimizing movements…

## Convergence of thresholding schemes for geometric flows – Tim Laux ( Max Planck Institute for Mathematics in the Sciences, Leipzig)

The thresholding scheme, a time discretization for mean-curvature flow was introduced by Meriman, Bence and Osher in 1992. In the talk we present new convergence results for modern variants of this scheme, in particular in the multi-phase case with…