Regularity at the free boundary for Dirac-harmonic maps from surfaces

2013/06/18 by Sharp, Ben, Zhu, Miaomiao
#35B65 #35J57 #35R35 #58J05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.4260

Abstract

We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces. Our methods also lead to the full interior ε-regularity and smooth estimates for weakly Dirac-harmonic maps in all dimensions.

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