## A priori estimates for elliptic equations in $\mathbb R^N$ – a critical case

Abstract: Using the Moser’s iteraction method we obtain an a priori estimate for elliptic equations in whole euclidian space in a critical growth situation

Read More## Dynamics of strongly interacting unstable two-solitons for generalized Korteweg-de Vries equations.

Abstract. Many evolution PDEs admit special solutions, called solitons, whose shape does not change in time. A multi-soliton is a solution which is close to a superposition of a finite number K of solitons placed at a large distance from each other. I am interested in describing multi-soliton dynamics for generalized Korteweg-de Vries equations. I will present a general method of formally predicting the time evolution of the centers and velocities of each soliton. Then I will discuss in detail the case K = 2, in particular in the regime of strong interactions, which occurs when the...

Read More## On the 3D Ginzburg-Landau model of superconductivity

Abstract: The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature is the occurrence of vortices (similar to those in fluid mechanics, but quantized), which appear above a certain value of the applied magnetic field called the first critical field. We are interested in the regime of small ɛ, where ɛ>0 is the inverse of the Ginzburg-Landau parameter. In this regime, the vortices are at main order codimension 2 topological singularities. In this talk I will present a quantitative 3D vortex approximation construction for the Ginzburg-Landau...

Read More## Existence of solutions to a pure critical elliptic system in a bounded domain

Abstract: http://capde.cl/past-seminars/

Read More## Gagliardo-Nirenberg-Sobolev inequalities in domains

Abstract: Our objective is to estimate constants for a type of Gagliardo-Nirenberg-Sobolev inequalities in domains in euclidean space. We obtain a rough bound valid for bounded convex domains in dimension 3 and higher. When the domain is a cube, we obtain an improved bound in any dimension. In one dimension, the sharp constant is simply related to the sharp constant of the inequality on the real line and I will comment on the open question whether this holds true in higher dimensions.

Read More