Colloquio De Giorgi 2021-2022

Differentiating in a non-differentiable environment

speaker: Nicola Gigli (SISSA Scuola Internazionale Superiore di Studi Avanzati )

abstract: We all know what the differential of a smooth map from R to R is. By looking at coordinates and then at charts, we also know what it is the differential of a smooth map between differentiable manifolds. With a little bit of work, we can also define a (weak) differential for Sobolev/BV maps in this setting (but the case of manifold-valued maps presents challenges already at this level). In this talk I will discuss how it is possible to differentiate maps between spaces that have no underlying differentiable structure at all. The concepts of Sobolev/BV maps in this setting will also be discussed.

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