We consider a variational model for two interacting species (or phases), subject to cross and self attractive interactions. We show existence and several qualitative properties of minimizers. Depending on the strengths of the attractive forces,…

# Categoria evento: Analysis Seminar

## Dynamic evolutions for a peeling test in dimension one. – Giuliano Lazzaroni (SISSA)

We present a simplified model of dynamic crack propagation, where the equation of elastodynamics is coupled with Griffith’s principle. In recent years there has been an increasing interest in studying systems where second-order equations for…

## Obstacle-Type Problems and Generalizations to the Fully Non-Linear Setting – Andreas Minne (Scuola Normale Superiore)

The obstacle problem is more than half a century old, but remains a relevant topic in mathematics due to the many variants and applications that occur in, for instance, physics, finance and potential theory. In the seminar we will briefly go over…

## From coarea formula to level set differential equations – Valentino Magnani (Universita’ di Pisa)

We present how the problem of coarea formula in the Heisenberg group leads us rather unexpectedly to a system of “level set differential equations”, generated by a defining mapping of very low regularity. In this system we cannot write classical…

## Minimal energy solutions and infinitely many bifurcating branches for a class of saturated nonlinear Schrödinger systems – Rainer Mandel (Centro De Giorgi)

In the talk I will prove existence and nonexistence results for finite energy solutions of some parameter-dependent saturated nonlinear Schrödinger system. It is shown that for most parameter samples the ground state solutions are semitrivial while…

## Nonlinear stability results for the Ohta-Kawasaki energy and for the nonlocal Mullins-Sekerka flow – Massimiliano Morini (Universita’ di Parma)

It has been recently shown that strictly stable critical configurations for the Ohta-Kawasaki energy are in fact isolated local minimizers with respect to small $L^1$-perturbations. After reviewing such results and some of their applications, we…

## Optimal bounds for mixtures of ferromagnetic interactions – Leonard Kreutz (GSSI (Gran Sasso Science Institute), L’Aquila)

We completely describe the effective surface tension of periodic mixtures of two types of ferromagnetic interactions. This problem is linked to optimal design of networks and their metric properties. This is joint work with A. Braides.…

## Crystal dislocation dynamics, collisions, relaxation times and asymptotics – Enrico Valdinoci

We consider an equation (or a system of equations) inspired by the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to…

## Boundary behavior and geometric properties of nonlocal minimal surfaces – Serena Dipierro

We recall the notion of nonlocal minimal surfaces and we discuss their qualitative and quantitative interior and and boundary behavior. In particular, we present some optimal examples in which the surfaces stick at the boundary. This phenomenon is…

## Phase segregation for binary mixtures of Bose-Einstein Condensates – Michael Goldman

In this talk I will discuss the (asymptotic) shape of the minimizers of a Gross-Pitaievskii functional describing Bose-Einstein condensates with two components. We will be interested in the regime of strong segregation where the two components do…