On De Giorgi’s lemma for variational interpolants in metric and Banach spaces
Alexander Mielke, Riccarda Rossi · ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2026
Variational interpolants are an indispensable tool for the construction of gradientflow 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.Drawing from this theory we study 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.For the latter we have to impose the condition of radial differentiability of the dissipation potential.Several examples are discussed to show how sharp the results are.