Care tutte, cari tutti,

la prossima settimana avremo due seminari di Analisi:

lunedì 29 aprile, alle ore 17:30 (+ merenda post-seminario) in aula seminari, avremo il piacere di ascoltare Luca Lussardi (Polito), che terrà un seminario https://www.dm.unipi.it/en/seminar/?id=66013124282479bbfbbaaac1 dal titolo “Nematic soap films”;

giovedì 2 maggio, alle ore 17 (+ merenda alle 16:45), in aula riunioni, avremo il piacere di ascoltare Giacomo Del Nin (Max-Planck-Institut, Lipsia), che terrà un seminario https://www.dm.unipi.it/en/seminar/?id=662778461ab535c3c8d5fa0c dai titolo "BMO-type seminorms and local Poincaré constants for BV functions".

Trovate qui sotto i due abstract. A presto, Ilaria Lucardesi e Luigi Forcella

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Dear all, next week, for the Mathematical Analysis Seminar, there will be two seminars:

on Monday 29th April at 5:30PM (+ snack after the seminar), in "Aula Seminari", we will have the pleasure of listening to Luca Lussardi (PoliTo). The title of the talk https://www.dm.unipi.it/en/seminar/?id=66013124282479bbfbbaaac1 https://www.dm.unipi.it/en/seminar/?id=6602fa9a282479bbfbbb1ff6 https://www.dm.unipi.it/en/seminar/?id=66013124282479bbfbbaaac1 is "Nematic soap films";

on Thursday 2nd May at 5PM (+ snack at 4:45PM), in "Aula Riunioni", we will have the pleasure of listening to Giacomo Del Nin (Max-Planck-Institut, Leipzig) . The title of the talkhttps://www.dm.unipi.it/en/seminar/?id=662778461ab535c3c8d5fa0c https://www.dm.unipi.it/en/seminar/?id=6617a944282479bbfbbf84a2 https://www.dm.unipi.it/en/seminar/?id=662778461ab535c3c8d5fa0c is "BMO-type seminorms and local Poincaré constants for BV functions".

Please find below the abstracts. See you soon, Ilaria Lucardesi and Luigi Forcella

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Speaker: Luca Lussardi (PoliTo) Title: Nematic soap films Abstract: Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. Some variational models for nematic films have been introduced by Giomi in 2012 and by Napoli and Vergori in 2018. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. The main difference between the two mentioned approaches is the way to compute the surface derivative of the nematic vector field. In this seminar I will briefly describe the models and I will present some recent analytical results obtained in collaboration with Giulia Bevilacqua, Chiara Lonati and Alfredo Marzocchi.

Speaker: Giacomo Del Nin (Max-Planck-Institut, Lipsia) Title: BMO-type seminorms and local Poincaré constants for BV functions Abstract: In 2015 Bourgain, Brezis, and Mironescu introduced a class of BMO-type functionals that measure the oscillation of a function on a family of disjoint ϵ-cubes. These functionals turned out to be related to the total variation of the function, and over the years several authors have addressed the problem of finding an expression for their limit as ϵ goes to zero. Thanks to the work of many, we now know that for SBV functions the limit exists and coincides with 1/2 times the jump variation plus 1/4 times the absolutely continuous variation. However, for BV functions with a non-trivial Cantor part, the limit might not exist. In this talk I will present a natural relaxation of these functionals that enforces the existence of the limit for any BV function. I will show that this limit is related to a quantity that we introduce, the local Poincarè constant of the function, and I will discuss some challenging open questions. This result is based on a project with Adolfo Arroyo-Rabasa (Bonn) and Paolo Bonicatto (Trento).