Calculus of Variations and Geometric Measure Theory

L. Brasco - F. Santambrogio

A note on some Poincaré inequalities on convex sets by Optimal Transport methods

created by brasco on 01 Jan 2016
modified on 14 Apr 2016


Accepted Paper

Inserted: 1 jan 2016
Last Updated: 14 apr 2016

Journal: Springer Proceedings in Mathematics & Statistics
Pages: 13
Year: 2016

The paper will be published in a volume for the proceedings of the 4th Italian-Japanese workshop on ``Geometric Properties for Parabolic and Elliptic PDE’s'', held in Palinuro in May 2015


We show that a class of Poincaré-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly unbounded.

Keywords: Wasserstein distances, Poincaré inequalities