# Dipartimento di Matematica - Università di Pisa

## Didattica

Text:

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MERCOLEDI' 16 MAGGIO 2012
17:00-18:00, Sala Seminari (Dip. Matematica)

SEMINARI DI CALCOLO DELLE VARIAZIONI E ANALISI GEOMETRICA
Rademacher's theorem for Euclidean measures
Andrea Marchese (Universita` di Pisa)

For every Euclidean Radon measure μ we state an adapted version of Rademacher's theorem, which is, in a certain sense, the best possible for the measure μ. We define a sort of fibre bundle (actually a map S that at each point x of Rn associates a vector subspace S(x) of TxRn, possibly with non-costant dimension k(x)) such that every Lipschitz function f:Rn→R is differentiable at x, along S(x), for μ-a.e. x. We prove that S is maximal in the following sense: there exists a Lipschitz function g:Rn→R which doesn't admit derivative at μ-a.e. x, along any direction not belonging to S(x). Joint work with Giovanni Alberti.

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Dipartimento di Matematica

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