Care tutte, cari tutti, la prossima settimana, nell’ambito del ciclo Seminari di Analisi, avremo il piacere di ospitare Raul Fernandes Horta – Universidade Federal de Minas Gerais (Brasile), che terrà un seminario<https://www.dm.unipi.it/en/seminar/?id=6916db5041e01ecbf88bc0ce> <https://www.dm.unipi.it/en/seminar/?id=6916db5041e01ecbf88bc0ce> dal titolo “Poincaré constants, fundamental frequencies and the isoanisotropic problem”. Il seminario si terrà mercoledì 21 gennaio alle ore 16, in Aula Magna. Trovate l’abstract qui sotto. A presto, Ilaria ----------------------------------- Dear all, next week, as part of the Analysis Seminar Series, we will have the pleasure of hosting Raul Fernandes Horta – Universidade Federal de Minas Gerais (Brazil), who will give a seminar<https://www.dm.unipi.it/en/seminar/?id=6916db5041e01ecbf88bc0ce> <https://www.dm.unipi.it/en/seminar/?id=6916db5041e01ecbf88bc0ce> entitled “Poincaré constants, fundamental frequencies and the isoanisotropic problem”. The seminar will take place on Wednesday, January 21 at 4 pm, in the Aula Magna. You will find the abstract below. See you soon, Ilaria ----------------------------------- Speaker: Raul Fernandes Horta - Universidade Federal de Minas Gerais (Brazil) Title: Poincaré constants, fundamental frequencies and the isoanisotropic problem Abstract: The first Dirichlet eigenvalue of the anisotropic p-laplacian (sometimes called fundamental frequency) has been vastly studied especially due to its variational characterization, which connects it to the Poincaré inequality. In this talk we study Poincaré constants that are defined using the characterization previously mentioned, however, unlike in the classical setting where the energy is given by a norm, here we allow it to be given by seminorms. This opens the question to when these constants are fundamental frequencies (eigenvalues of the Euler-Lagrange equation) of their corresponding operators. Finally, we talk about the isoanisotropic problem, which is an optimization problem that consists of finding seminorms that either maximize or minimize the Poincaré constants. This can be seen as a counterpart of the celebrated isoperimetric Faber-Krahn inequality, which states that the domain that minimizes the fundamental frequency is the ball.