Seminario EDP UAM-ICMAT
Calibrations for nonlocal elliptic functionals
Ponente: Iñigo U. Erneta (Rutgers University)Fecha: viernes 11 de octubre de 2024 - 12:30Lugar: Aula Gris 1, ICMAT
Resumen:
The Calculus of Variations deals with the minimization of functionals. While every minimizer satisfies the associated Euler-Lagrange equation, the converse is not true in general. To show that a solution is a minimizer typically involves building a “calibration", namely, a null-Lagrangian satisfying certain additional properties. For classical (local) equations, such a construction is well-known and goes back to the celebrated Weierstrass theory of extremal fields.
In this talk, I will describe some recent works with X. Cabré and J.C. Felipe-Navarro where we extend the construction of calibrations to the nonlocal setting. I will first give an overview of the classical theory of calibrations and its relation to fields of extremals. Our novel analysis of the local case will then lead us to a natural nonlocal analogue of the calibration. I will conclude by explaining several relevant applications of our construction.
