WIAS Preprint No. 3127, (2024)

On De Giorgi's lemma for variational interpolants in metric and Banach spaces


Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261

2020 Mathematics Subject Classification

  • 34G20 47J20 49J40 49J53 49S05 58E30

Keywords

  • Generalized gradient systems, minimizing movement scheme, variational interpolants, discrete energy-dissipation inequality, radial differentiabilit

DOI

10.20347/WIAS.PREPRINT.3127

Abstract

Variational interpolants are an indispensable tool for the construction of gradient-flow solutions via the Minimizing Movement Scheme. De Giorgi's 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.

Download Documents