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arXiv · 2402.07308

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

Harald Hanche-Olsen·Helge Holden
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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.

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Harald Hanche-Olsen, Helge Holden. 2024-02-11. The Aubin-Lions-Dubinskii theorems on compactness in Bochner spaces. https://arxiv.org/abs/2402.07308

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