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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

Analía Silva (Imasl - Universidad Nacional de San Luis)

A mass transportation approach for Sobolev inequalities in variable exponent spaces

The existence of a transport between two probability measures and that this transport is the gradient of a convex function can be used to prove geometric and functional inequalities. For example, in 2004, Cordero-Erasquin, Nazaret and Villani give a proof of the Sobolev critical inequalities as application of mass transportation techniques. The objective of this talk is to show how extend these ideas in the context of variable exponent spaces. Joint work Juan Pablo Borthagaray (UBA- IMAS) and Julián Fernández Bonder (UBA-IMAS).