English

The Aubin-Lions-Dubinskii theorems on compactness in Bochner spaces

Analysis of PDEs 2024-11-19 v2 Functional Analysis

Abstract

A fundamental issue in the theory of time-dependent differential equations is to characterize precompact sets in Bochner spaces. We here survey the theory, starting with the classical Aubin-Lions inequality and its important extension by Dubinskii. In particular, we give a simple and self-contained proof of the compactness result due to Chen, Jungel, and Liu.

Keywords

Cite

@article{arxiv.2402.07308,
  title  = {The Aubin-Lions-Dubinskii theorems on compactness in Bochner spaces},
  author = {Harald Hanche-Olsen and Helge Holden},
  journal= {arXiv preprint arXiv:2402.07308},
  year   = {2024}
}