1
$\begingroup$

Theorem 5 p.84 of J. Simons paper "Compact sets in the space $L^p(0,T;B)$" states a generalization of the Aubin-Lions lemma which relaxes the required regularity in time to the existence of a modulus of continuity in time or as in Corollary 5 (after Theorem 5) to fractional Sobolev in time for $s<1$ (usual Aubin-Lions requires $s=1$).

I am not really familiar with moduli of continuity and I would like to see examples of the Theorem mentioned above. Everything I discovered so far uses the standard Aubin-Lions with $s=1$.

Improve this question
$\endgroup$
2
  • $\begingroup$ Just to clarify, you are asking for examples where Simon's generalization(s) of the classical Aubin-Lions Lemma are used and the latter is not applicable, right? $\endgroup$
    – Hannes
    Commented Mar 24, 2023 at 12:39
  • $\begingroup$ Yes, for instance because a full time derivative in some $L^p$ or $W^{-r,p}$ is not available. $\endgroup$
    – Jakob Möller
    Commented Mar 25, 2023 at 8:49

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .