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

Viernes, 1 de diciembre de 2023, 12:00h., Módulo 17, Aula 520
Enlace online: youtube.com/live/C-dNE3qtxd0
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Abstract: 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.