WIAS Preprint No. 3022, (2023)

An introduction to the analysis of gradients systems


Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2020 Mathematics Subject Classification

  • 35-02 49-02 35K55 47H05

Keywords

  • Gradient-flow equations, dissipation potential, kinetic relation, Fenchel equivalences, Fréchet subdifferentials, time-incremental minimization, abstract chain rule, energy-dissipation balance, energy-dissipation principle, minimizing movements, metric slope and metric speed, curves of maximal slope, De Giorgi lemma,, evolutionary Gamma-convergence

DOI

10.20347/WIAS.PREPRINT.3022

Abstract

The present notes provide an extended version of a small lecture course (of 36 hours) given at the Humboldt-Universität zu Berlin in the Winter Term 2022/23. The material starting in Section 5.4 was added afterwards. The aim of these notes to give an introductory overview on the analytical approaches for gradient-flow equations in Hilbert spaces, Banach spaces, and metric spaces and to show that on the first entry level these theories have a lot in common. The theories and their specific setups are illustrated by suitable examples and counterexamples.

Download Documents