March 2023 - Analysis-seminar - Mailing list — Dipartimento di Matematica, UniPI

seminario di Francesca Prinari, giovedì ore 17
by Alessandra Pluda 28 Mar '23

28 Mar '23

Cari tutti, questa settimana ci sarà un seminario di analisi di Francesca Prinari (UNIPI): Giovedì 30 Marzo Aula Riunioni, ore 17:00 Seguono titolo e abstract. Un caro saluto, Alessandra, Jacopo e Maria Stella. Titolo: Sobolev embedding and distance functions Abstract: On a general open set of the euclidean space, we study the relation between the embedding of the homogeneous Sobolev space $D^{1,p}_0$ into $L^q$ and the summability properties of the distance function. We prove that in the superconformal case (i.e. when $p$ is larger than the dimension) these two facts are equivalent, while in the subconformal and conformal cases (i.e. when p is less than or equal to the dimension) we construct counterexamples to this equivalence. In turn, our analysis permits to study the asymptotic behaviour of the positive solution of the Lane-Emden equation for the p-Laplacian with sub-homogeneous right-hand side, as the exponent p diverges to $+\infty$. (a joint work with L. Brasco and A.C. Zagati).

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Giornata di seminari dei dottorandi e perfezionandi in analisi
by Alessandra Pluda 22 Mar '23

22 Mar '23

Cari tutti, settimana prossima ci sarà una giornata dedicata a seminari di nostri dottorandi e perfezionandi di analisi. https://www.dm.unipi.it/en/giornata-di-seminari-dei-dottorandi-e-perfeziona… Vi copio schedule, titoli e abstract. Un caro saluto, Alessandra Mercoledì 29 marzo 2023 Mattina: Aula Magna – Dipartimento di Matematica 9:00-9:45 Lorenzo Ferreri Asymptotic properties of an optimal principal eigenvalue with dirichlet boundary conditions 9:45-10:30 Michele Caselli Non-local approximation of minimal surfaces and existence of infinitely many minimal surfaces in 3-manifolds 11:00-11:45 Daniele Barbera L^p-L^q Maximal Regularity estimate for the Beris-Edward model in the half-plane 11:45-12:30 Mattia Freguglia Alcuni problemi riguardanti l’approssimazione diffusa del funzionale elastica Pomeriggio: Aula Fermi – Scuola Normale Superiore 14:00-14:45 Claudio Afeltra TBA 14:45-15:30 Camillo Brena Introduzione agli spazi RCD 16:00-16:45 Nicola Picenni How to recognize constant functions through nonlocal functionals Daniele Barbera (UNIPI) L^p-L^q Maximal Regularity estimate for the Beris-Edward model in the half-plane In this seminar we will consider the Beris-Edward model for the study of nematic liquid crystals in the half-plane R^N_+ with N\ge 2. Using the L^p-L^q Maximal Regularity Theory, we will prove the existence and uniqueness of a solution for the resolvent system and the corresponding existence and uniqueness of the solution for the linear evolution problem for p,q\in(1,\infty). As an application, we will see the existence of a local solution for the general model for small initial data for p>2 and q>N. Camillo Brena (SNS) Introduzione agli spazi RCD Lo scopo di questo seminario è di introdurre brevemente gli spazi RCD. Inizierò con un esempio che motiva l’interesse verso l’analisi in ambiente non-liscio per poi definire gli spazi RCD ed esporne le proprietà più rilevanti Michele Caselli (SNS) Non-local approximation of minimal surfaces and existence of infinitely many minimal surfaces in 3-manifolds In this talk, I will describe a possible path towards a proof of Yau's conjecture (on the existence of infinitely many minimal surfaces in every Riemannian 3-manifold) based on nonlocal approximation of minimal surfaces. On one hand, in a work in preparation with J. Serra and E. F. Simon, we show that the analog of Yau's conjecture for nonlocal minimal surfaces holds. This is because Morse theory for nonlocal minimal surfaces seems to be flawless as finite-dimensional Morse theory, at least from the compactness perspective. On the other hand, in a recent work by H. Chang, S. Dipierro, J. Serra, and E. Valdinoci the authors prove that one can successfully pass nonlocal minimal surfaces to the limit to obtain classical minimal surfaces, keeping strong curvature and separation estimates. These two works seem to point to the fact that one could recover Yau's conjecture from its nonlocal analog. Lorenzo Ferreri (SNS) Asymptotic properties of an optimal principal eigenvalue with dirichlet boundary conditions We consider a weighted eigenvalue problem for the Dirichlet laplacian in a smooth bounded domain Ω ⊂ R^N , where the bang-bang weight equals a positive constant m on the favourable region E ⊂ Ω and a negative constant −m on Ω \ E. The corresponding positive principal eigenvalue provides a threshold to detect persis- tence/extinction of a species whose evolution is described by the heterogeneous Fisher-KPP equation in population dynamics. In particular, we study the minimization of such eigen- value with respect to the shape and position of E in Ω. We provide a sharp asymptotic expansion of the optimal principal positive eigenvalue and a sharp spherical asymmetry estimate of the optimal favourable regions in the singularly perturbed regime in which the volume of E vanishes. In particular, we deduce that, up to subsequences, the optimal regions E concentrate at a point maximizing the distance from ∂Ω. This is a joint work with Gianmaria Verzini Mattia Freguglia (SNS) Alcuni problemi riguardanti l’approssimazione diffusa del funzionale elastica In questo seminario parlerò di una congettura proposta da Bellettini e Paolini come variante di una congettura precedente di De Giorgi sulla possibilità di approssimare, nel senso della Gamma-convergenza, in modo diffuso la somma del funzionale Perimetro e del funzionale di Willmore su insiemi con bordo di classe C^2. Questo problema è stato risolto da Röger e Schätzle in dimensione n=2,3 e indipendentemente da Nagase e Tonegawa in dimensione n=2, ma rimane aperto in dimensione più alta. Dopo aver introdotto il problema mi concentrerò sul caso n=2 e discuterò le difficoltà che emergono provando a estendere il risultato a insiemi meno regolari. Alla fine proporrò un possibile candidato a essere il Gamma-limite dei funzionali diffusi su tutto L^1 spiegando quali sarebbero gli step mancanti per ottenere una dimostrazione. Nicola Picenni (SNS) How to recognize constant functions through nonlocal functionals We describe a problem proposed by H. Brezis concerning the characterization of constant functions through double integrals that involve their difference quotients. In particular, we focus on the problem of finding necessary and sufficient conditions under which such characterization holds true. We present and motivate a natural necessary condition proposed by R. Ignat and we show with a counterexample that it is not sufficient. On the other hand, we describe some additional conditions under which the answer to the question turns out to be postive. Finally, we discuss many intermediate cases that remain open, and how they motivate further questions in measure theory. Some parts of the talk are based on a joint work with M. Gobbino.

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International Conference on Partial Differential Equations and Applications in honor of the 70th birthday of Pierangelo Marcati
by Luigi Forcella 17 Mar '23

17 Mar '23

Buon pomeriggio a tutte e a tutti, Inoltro il seguente annuncio di una conferenza che si terrà a L’Aquila nei giorni 19-23 Giugno 2023, e che abbiamo organizzato in occasione dei 70 anni del Professor Pierangelo Marcati. Luigi. --------------- Dear colleagues, we are pleased to announce the “International Conference on Partial Differential Equations and Applications in honor of the 70thbirthday of Pierangelo Marcati”, which will be held at the GSSI - Gran Sasso Science Institute, L’Aquila (Italy) in the period 19-23/06/2023. The conference is in honor of our dear friend and colleague Pierangelo Marcati for his 70th birthday and aims at celebrating his scientific contributions and his constant commitment to the academic community. The aim of the meeting is to gather leading experts and researchers to propose and discuss new ideas in the field of Partial Differential Equations and their applications. The list of confirmed speakers, as well as other relevant information, may be found in the webpage of the conference: https://indico.gssi.it/event/486/<https://es.sonicurlprotection-fra.com/click?PV=2&MSGID=20230317120236016256…>. Registration is free, but mandatory, and it is now open. The deadline for registering to the school is Sunday, June 4th 2023. Best regards, Debora Amadori (UnivAQ), Paolo Antonelli (GSSI), Marco Di Francesco (UnivAQ), Federica Di Michele (INGV), Donatella Donatelli (UnivAQ), Luigi Forcella (UniPi), Corrado Lattanzio (UnivAQ), Michele Palladino (UnivAQ), Bruno Rubino, (UnivAQ), Stefano Spirito (UnivAQ) ==== Apologies for multiple posting ==== ----------- Luigi Forcella, Assistant Professor (RTD-B, tenure-track) University of Pisa Department of Mathematics Largo Bruno Pontecorvo 5 57127 Pisa, Italy https://pagine.dm.unipi.it/forcella/index.html

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annullamento Colloquium Carlos Kenig
by Maria Stella Gelli 12 Mar '23

12 Mar '23

Cari tutti, purtroppo il Colloquium di Carlos Kenig previsto per martedi' prossimo alle ore 17 non si potrà tenere dato che lo speaker non potrà raggiungere Pisa come previsto a causa di uno sciopero delle compagnie aeree che partono da Berlino. Tenteremo di riproporre appena possibile il seminario previsto ma dati i numerosi impegni del Prof. Kenig ciò potrebbe non avvenire in tempi brevi. Cari saluti Maria Stella Gelli (a nome anche di Paola Boito e Francesco Sala)

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due seminari
by Alessandra Pluda 05 Mar '23

05 Mar '23

Cari tutti, vi ricordo dei due seminari dell'8 e 9 marzo. Mercoledì 8 marzo, nell'ambito dei seminari VAREG, abbiamo Damià Torres (UAB) Optimal regularity for supercritical parabolic obstacle problems https://www.dm.unipi.it/eventi/optimal-regularity-for-supercritical-parabol… ore 18:00 Aula Magna Invece Giovedì 9 marzo ci sarà un seminario di Analisi di Tohru Ozawa (Waseda) Proof of Sobolev and related inequalities via heat semigroup https://www.dm.unipi.it/eventi/?yy=2023&mm=3&dd=9 ore 17:00 Sala Seminari. A presto, Alessandra

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