Care tutte, cari tutti,
per il prossimo evento del ciclo dei Seminari di Analisi, giovedì 14 novembre alle ore 17, in Aula Magna, avremo il piacere di ascoltare Bohdan Bulanyi (Università di Bologna), che terrà un seminario https://www.dm.unipi.it/en/seminar/?id=66d8284224a587d54c10bbbb dal titolo "Limiting behavior of minimizing $p$-harmonic maps in 3d as $p$ goes to $2$ with finite fundamental group". Trovate l'abstract qui sotto.
A presto, Ilaria Lucardesi e Luigi Forcella
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Dear all, on Thursday November 14th at 5PM, in "Aula Magna", for the Mathematical Analysis Seminar, we will have the pleasure of listening to Bohdan Bulanyi (Università di Bologna). The title of the talk is "Limiting behavior of minimizing $p$-harmonic maps in 3d as $p$ goes to $2$ with finite fundamental group". Please find the abstract below.
See you soon, Ilaria Lucardesi and Luigi Forcella
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Speaker: Bohdan Bulanyi (Università di Bologna)
Title: Limiting behavior of minimizing $p$-harmonic maps in 3d as $p$ goes to $2$ with finite fundamental group.
Abstract: The presentation will focus on some new results concerning the limiting behavior of minimizing $p$-harmonic maps from a bounded Lipschitz domain $\Omega \subset \mathbb{R}^{3}$ to a compact connected Riemannian manifold without boundary and with finite fundamental group as $p \nearrow 2$. We prove that there exists a closed set $S_{*}$ of finite length such that minimizing $p$-harmonic maps converge to a locally minimizing harmonic map in $\Omega \setminus S_{*}$. We prove that locally inside $\Omega$ the singular set $S_{*}$ is a finite union of straight line segments, and it minimizes the mass in the appropriate class of admissible chains. Furthermore, we establish local and global estimates for the limiting singular harmonic map. Under additional assumptions, we prove that globally in $\overline{\Omega}$ the set $S_{*}$ is a finite union of straight line segments, and it minimizes the mass in the appropriate class of admissible chains, which is defined by a given boundary datum and $\Omega$. In this talk, I will try to give an overview of these results. This is a joint work with Jean Van Schaftingen and Benoît Van Vaerenbergh.