Some variants of the classical Aubin–Lions Lemma

By Ayman Moussa. 2014

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This paper explores two generalizations of the classical Aubin–Lions Lemma. First, we give a sufficient condition to commute weak limit and multiplication of two functions. We deduce from this criteria a compactness theorem for degenerate parabolic equations. Second, we state and prove a compactness theorem for noncylindrical domains, including the case of dual estimates involving only divergence-free test functions.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/993e82ceea4bfbfbcebd8988c4d22123ea1164ae