COLOQUIO DE OTOÑO DEL DEPARTAMENTO

Viernes, 1 de diciembre de 2023
12:00 h., Módulo 17 - Aula 520 (Dpto. Matemáticas UAM),
y además ONLINE - URL: https://youtube.com/live/C-dNE3qtxd0

Xavier Cabré
ICREA and UPC (Catalunya)

Hilbert’s 19th problem on the regularity
of minimizers to elliptic functionals:
minimal surfaces and reaction-diffusion
equations

Hilbert’s 19th problem asked whether minimizers of elliptic functionals are
always analytic. In this lecture I will describe progress made on the problem
since the late fifties. After explaining the celebrated result of De Giorgi and
Nash, we will focus on minimal surfaces, from the developments in the late
sixties to the recent important work of Chodosh and Li. In the last part of the
lecture, I will concentrate on a recent result (joint with Figalli, Ros-Oton, and
Serra) for reaction-diffusion equations. As in minimal surfaces theory, smoothness
of stable solutions (and of minimizers) only holds up to a certain critical
space dimension.