ε-regularity for systems involving non-local, antisymmetric operators

2012/05/13 by Armin Schikorra · 4 citations
Mathematics · #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.1007/s00526-015-0913-3

arxiv created 2012/05/13 · openalex publication_date 2015/08/19 · arxiv updated 2015/08/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

We prove an epsilon-regularity theorem for critical and super-critical systems with a non-local antisymmetric operator on the right-hand side. These systems contain as special cases, Euler-Lagrange equations of conformally invariant variational functionals as Rivière treated them, and also Euler-Lagrange equations of fractional harmonic maps introduced by Da Lio-Rivière. In particular, the arguments presented here give new and uniform proofs of the regularity results by Rivière, Rivière-Struwe, Da-Lio-Rivière, and also the integrability results by Sharp-Topping and Sharp, not discriminating between the classical local, and the non-local situations.

Citations

• Hp spaces of several variables
• Decay estimates for Rivière's equation, with applications to regularity and compactness

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• A regularity theory for intrinsic minimising fractional harmonic maps
• Compactness and Bubbles Analysis for 1/2-harmonic Maps
• Horizontal α-Harmonic Maps
• Sharp commutator estimates via harmonic extensions

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