Calculus of Variations and Geometric Measure Theory
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Sobolev calculus on weighted Euclidean spaces

Danka Lučić (Università di Pisa)

created by gelli on 19 Nov 2020

25 nov 2020 -- 17:00   [open in google calendar]

Dipartimento di Matematica (online)

In order to join the seminar, please fill in the mandatory participation form before November 24th. Further information and instructions will be sent afterwards to the online audience.

Abstract.

The study of the Sobolev space over weighted Euclidean spaces (i.e. equipped with an arbitrary Radon measure) has been initiated in the late nineties, motivated by various applications in the field of the Calculus of Variations. Two important approaches were introduced by Bouchitté-Buttazzo-Seppecher and Zhikov, both relying upon a notion of 'Sobolev tangent bundle'. In this talk, we will prove the equivalence of these two theories, by employing a third notion of Sobolev space due to Ambrosio-Gigli-Savaré, which comes from the more general setting of analysis on metric measure spaces. Moreover, we will investigate the relation between the above-mentioned 'Sobolev tangent bundle' and the 'Lipschitz tangent bundle' introduced by Alberti-Marchese. Finally, we will provide necessary and sufficient conditions for the Sobolev-Lipschitz tangent bundles to have full rank.

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