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English version below! <<<

Carə tuttə,

Vi annuncio il prossimo seminario MAP:

*--> Speaker:* Nicola Picenni

*--> Data:* Giovedì 19 ottobre, ore 11:30

*--> Dove:* Aula Seminari del Dipartimento di Matematica (Pisa) e Online su Gmeet:

Nicola Picenni (seminarimap.wixsite.com) https://seminarimap.wixsite.com/seminarimap/articoli/nicola-picenni

*--> Titolo:* Non-local functionals converging to Sobolev and BV norms

*--> Abstract:* During the last twenty years, inspired by the famous "BBM formula", many non-local characterizations of Sobolev and BV spaces have been studied in the literature. These characterizations usually rely on the limit (or the Gamma-limit) of suitable non-local functionals involving difference quotients instead of derivatives. In the first part of the talk, we present a simple proof of the "BBM formula", based on the sectioning technique, which provides both the pointwise and the Gamma-convergence. Then, in the second part of the talk, we describe some recent developments in this field. In particular we consider a general class of functionals introduced by Brezis, Seeger, Van Schaftingen and Yung, and we discuss some recent results and open questions related with these functionals.

Ricordiamo che questi seminari sono aperti a tuttə: la prima metà del seminario introduce i concetti e gli strumenti necessari per la seconda metà, dedicata agli argomenti di ricerca.

Per altre informazioni, visitate il nostro sito: https://seminarimap.wixsite.com/seminarimap

A presto,

Gli organizzatori: Daniele Barbera Jeremy Mirmina Mario Rastrelli Leonardo Roveri Luciano Sciaraffia

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English Version <<<

Dear all,

Here the announcement of the next MAP seminar:

*--> Speaker:* Nicola Picenni

*--> Date:* Thursday 19th October, at 11:30

*--> Where:* Aula Seminari, Dipartimento di Matematica (Pisa) and Online on Gmeet:

Nicola Picenni (seminarimap.wixsite.com) https://seminarimap.wixsite.com/seminarimap/articoli/nicola-picenni

*--> Title:* Non-local functionals converging to Sobolev and BV norms

*--> Abstract:* During the last twenty years, inspired by the famous "BBM formula", many non-local characterizations of Sobolev and BV spaces have been studied in the literature. These characterizations usually rely on the limit (or the Gamma-limit) of suitable non-local functionals involving difference quotients instead of derivatives. In the first part of the talk, we present a simple proof of the "BBM formula", based on the sectioning technique, which provides both the pointwise and the Gamma-convergence. Then, in the second part of the talk, we describe some recent developments in this field. In particular we consider a general class of functionals introduced by Brezis, Seeger, Van Schaftingen and Yung, and we discuss some recent results and open questions related with these functionals.

We remind that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

For more information, check our website:

https://seminarimap.wixsite.com/seminarimap

See you soon,

The organizers: Daniele Barbera Jeremy Mirmina Mario Rastrelli Leonardo Roveri Luciano Sciaraffia

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