Some variants of the classical Aubin-Lions Lemma

Abstract

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. Secondly, we state and prove a compactness Theorem for non-cylindrical domains, including the case of dual estimates involving only divergence-free test functions.

References in corpus (1)

• A note on the uniformity of the constant in the Poincaré inequality

Cited by in corpus (1)

• Convergence in $C([0,T];L^2(\Omega ))$ of weak solutions to perturbed doubly degenerate parabolic equations