"Asymptotic behaviour of sequences of elliptic and parabolic monotone operators depending on vector fields"

Titolo: Asymptotic behaviour of sequences of elliptic and parabolic monotone operators depending on vector fields

Abstract: In this talk, I present recent results obtained in collaboration with Fabio Paronetto and Eugenio Vecchi concerning variational convergences for differential operators depending on a family of Lipschitz continuous vector fields X. I will focus, in particular, to H-compactness (or G-compactness) results for a class of monotone operators both elliptic and parabolic. This theory, known as “compensated compactness”, was initiated by François Murat and Luc Tartar in the Euclidean case and to date it still finds numerous applications. Here we try to extend the Murat-Tartar H-compactness theorem for monotone operators to a class of operators depending on the family X, under suitable assumptions on X. I will provide many examples of relevant families of suitable vector fields and at least an example in which the standard theory seems not to be applicable.

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