Ilaria
Lucardesi e Luigi Forcella
---------------------------------------------
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
---------------------------------------------
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.