The De Giorgi Lemma `through spaces': from a topological to a Banach framework

par Riccarda Rossi (Brescia)

mercredi 11 mars 2026, 09:00 → 10:30 Europe/Paris

112 (Braconnier)

Variational interpolants are an indispensable tool for the construction of gradient- flow solutions via the Minimizing Movement Scheme. The De Giorgi lemma provides the associated discrete energy-dissipation inequality. It was originally developed for metric gradient systems.
In this talk, I will first discuss its generalization to topological spaces. Secondly, I will examine the case of generalized gradient systems in Banach spaces, where a refined theory allows us to extend the validity of the discrete energy-dissipation inequality and to establish it as an equality in qualified situations.
 
 Based on joint works with Giuseppe Savaré and Alexander Mielke.