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arXiv · 2306.05026

An introduction to the analysis of gradients systems

Alexander Mielke
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Abstract

The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). 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.

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Alexander Mielke. 2023-06-08. An introduction to the analysis of gradients systems. https://arxiv.org/abs/2306.05026

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