Care tutte, cari tutti,
per il prossimo evento del ciclo dei Seminari di Analisi, giovedì 7 novembre alle ore 17, in Aula Riunioni, avremo il piacere di ascoltare Simone Cito (Università del Salento), che terrà un seminario https://www.dm.unipi.it/en/seminar/?id=66d8284224a587d54c10bbbb dal titolo "A stability result for the first Robin-Neumann eigenvalue with negative boundary parameter: a double perturbation approach". Trovate l'abstract qui sotto.
Il seminario sarà preceduto da una merenda alle 16:45 nella stessa aula.
A presto, Ilaria Lucardesi e Luigi Forcella
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Dear all, on Thursday November 7th at 5PM, in "Aula Riunioni", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Simone Cito (Università del Salento). The title of the talkhttps://www.dm.unipi.it/en/seminar/?id=66d8284224a587d54c10bbbb is "A stability result for the first Robin-Neumann eigenvalue with negative boundary parameter: a double perturbation approach". Please find the abstract below.
The seminar will be preceded by a snack in the same room, starting at 4:45 PM.
See you soon, Ilaria Lucardesi and Luigi Forcella
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Speaker: Simone Cito (Università del Salento)
Title: A stability result for the first Robin-Neumann eigenvalue with negative boundary parameter: a double perturbation approach
Abstract: Let $\Omega=\Omega_0\setminus\overline{\Theta}\subset\R^n$ ($n\ge 2$) such that $\Omega_0$ is open and convex and $\Theta$ is a finite union of open sets homeomorphic to balls. We consider the eigenvalue problem for the Laplace operator associated to $\Omega$, with Robin boundary condition with parameter $\beta<0$ on $\partial \Omega_0$ and Neumann boundary condition on $\partial \Theta$. In 2020, G. Paoli, G. Piscitelli and L. Trani proved that the spherical shell is the only maximizer for the first Robin-Neumann eigenvalue in the class of domains $\Omega$ with fixed volume and outer perimeter.
In this seminar we present the quantitative version of the afore-mentioned isoperimetric inequality and recall some previous stability results involving the Robin condition with negative boundary parameter. The main novelty when dealing with sets of the type $\Omega=\Omega_0\setminus \overline{\Theta}$ consists in the introduction of a new type of hybrid asymmetry, that takes into account the different boundary conditions on $\partial\Omega_0$ and $\partial \Theta$. Up to our knowledge, in this context, this is the first stability result in which \emph{both} the outer and the inner boundary are perturbed.
The talk is based on some results obtained in collaboration with D.A. La Manna (Università degli Studi di Napoli Federico II), G. Paoli (Università degli Studi di Napoli Federico II) and G. Piscitelli (Università degli Studi di Napoli Parthenope).