Renormalized energies for unit-valued harmonic maps in multiply connected domains
Rémy Rodiac, Paúl Ubillús · Asymptotic Analysis · 2021
In this article we derive the expression of renormalized energies for unit-valued harmonic maps defined on a smooth bounded domain in [Formula: see text] whose boundary has several connected components. The notion of renormalized energies was introduced by Bethuel–Brezis–Hélein in order to describe the position of limiting Ginzburg–Landau vortices in simply connected domains. We show here, how a non-trivial topology of the domain modifies the expression of the renormalized energies. We treat the case of Dirichlet boundary conditions and Neumann boundary conditions as well.