Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary
Jürgen Jost
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany, Department of Mathematics, Leipzig University, 04081 Leipzig, GermanyLei Liu
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, GermanyMiaomiao Zhu
School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China
Abstract
For a sequence of coupled fields from a compact Riemann surface M with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up process near the boundary. As an application to the heat flow of Dirac-harmonic maps from surfaces with boundary, when such a flow blows up at infinite time, we obtain an energy identity.
Cite this article
Jürgen Jost, Lei Liu, Miaomiao Zhu, Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 365–387
DOI 10.1016/J.ANIHPC.2018.05.006