# Seminario di Equazioni Differenziali e Applicazioni: Differentiability of Lipschitz functions with respect to measures

## Giovedì 27 Marzo 2014, ore 12:00 - Aula 1BC45 - Andrea Marchese

ARGOMENTI: Seminari

SEMINARIO DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI

Giovedì 27 Marzo 2014 alle ore 12:00 in aula 1BC45, Andrea Marchese (Max-Planck-Institut fur Mathematik, Leipzig) terrà un seminario dal titolo "Differentiability of Lipschitz functions with respect to measures".

Abstract
In this talk I will give an overview on the recent works about the optimality of this result and I will show an extension of the theorem, when the Lebesgue measure is replaced by an arbitrary measure $mu$. I will explain how to associate to $mu$ a bundle of vector spaces such that every Lipschitz function is differentiable at $mu$-a.e. point along the corresponding vector space. I will also show that this bundle is the smallest possible among those with the described property, exhibiting a Lipschitz function which is $mu$-a.e. non differentiable along any direction which does not lie in the bundle.
This is joint work with Giovanni Alberti.

Rif. Int. M. Bardi, E. Feleqi, D. Vitone