A weak energy identity for (n+α)-harmonic maps with a free boundary in a sphere

2025/03/27 by Martino, Dorian, Mazowiecka, Katarzyna, Rodiac, Rémy
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.21523

Abstract

In this article, we show that sequences of (n+α)-harmonic maps with a free boundary in \mathbb S^d-1, where α is a parameter tending to zero, converge to a bubble tree. For such sequences, we prove in detail that the limiting energy is equal to the energy of the macroscopic limit plus the sum of the energies of certain ``bubbles'', each multiplied by a corresponding coefficient.

Related

• Energy identity for approximations of harmonic maps from surfaces
• Energy Identity for Stationary Harmonic Maps
• Bubble tree convergence for harmonic maps into compact locally CAT(1)\n spaces
• Low-energy α-harmonic maps into the round sphere
• Low energy levels of harmonic maps into analytic manifolds