We present a survey of nonlinear elliptic equations with nonlocal interactions. These equations describe the collective behavior of self-interacting many-body systems at different scales, from atoms a...
Society's ever-increasing integration of autonomous systems in day-to-day life has simultaneously brought forth concerns as to how their safety and reliability can be verified. To this end, reachable ...
Abstract: For a uniform magnetic field, we provide a decomposition of operators commuting with the associated magnetic translations. As an application, we rewrite the energy per unit surface for an el...
We will consider a type of cooperative nonlinear elliptic system in R^N. The interest of this problem is based on the presence of Sobolev or Sobolev-Hardy critical power nonlinearities and a nonlinear...
Let G be a reductive connected group over an algebraically closed field of characteristic p . Of particular importance in the study of G is the set u(G) of unipotent conjugacy classes. It is known tha...
The dynamics of variable-in-shape drug particles are fundamental to predict the dissolution of drugs in a fluid. In this talk we propose a new approach which consists of describing the dissolution pro...
We consider maps between spheres \(S^n\) to \(S^\ell\) that minimize the Sobolev-space energy \(W^{s,n/s}\) for some \(s \in (0,1)\) in a given homotopy class. The basic question is: in which homotopy...
Abstract: Metastability phenomena show up in the dynamical behavior of a large variety of complex real world systems. From a mathematical point of view the dynamics of such systems may be modeled by m...
Abstract: I will discuss the existence of turbulent solutions to a quantum hydrodynamic (QHD) system, with periodic boundary conditions. A suitable nonlinear change of variables (the Madelung transfor...
The Brauer group, classifying Azumaya algebras up to Morita equivalence, is a fundamental invariant in number theory and algebraic geometry. Given a moduli problem M (e.g. smooth curves of a given gen...
We consider general two-dimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular f...
