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Chiffres clefs

217 personnes travaillent au LJLL

83 personnels permanents

47 enseignants chercheurs

13 chercheurs CNRS

9 chercheurs INRIA

2 chercheurs CEREMA

12 ingénieurs, techniciens et personnels administratifs

134 personnels non permanents

85 doctorants

16 post-doc et ATER

5 chaires et délégations

12 émérites et collaborateurs bénévoles

16 visiteurs


Chiffres janvier 2014


Séminaire du LJLL - 06 10 2017 14h00 : G. De Philippis

Guido De Philippis (Ecole Internationale Supérieure d’Etudes Avancées, Trieste)
On the converse of Rademacher’s Theorem and the set of good measures in Lipschitz differentiability spaces

Rademacher’s Theorem asserts that every Lipschitz function on R^N is differentiable almost everywhere with respect to the Lebesgue measure. This result has been extended by Pansu to Carnot’s groups and by Cheeger to abstract metric measure spaces which are now called "Lipschitz differentiability spaces". A natural question is then to identify the set of all the "good measures” on metric spaces for which every Lipschitz function is differentiable almost everywhere.
The aim of this talk will be to discuss this issue in increasing generality. In particular we will present a proof of the fact that in R^N Rademacher’s Theorem holds for a measure if and only if this measure is absolutely continuous with respect to the Lebesgue measure. This result is based on a new structural result for measures satisfying a PDE constraint.
We will also show some consequences of this structural result concerning Lipschitz differentiability spaces. We will finally discuss some ongoing work concerning the converse of Pansu’s Theorem.