Regularity of n/2-harmonic maps into spheres

Abstract

We prove Hoelder continuity for n/2-harmonic maps from subsets of Rn into a sphere. This extends a recent one-dimensional result by F. Da Lio and T. Riviere to arbitrary dimensions. The proof relies on compensation effects which we quantify adapting an approach for Wente's inequality by L. Tartar, instead of Besov-space arguments which were used in the one-dimensional case. Moreover, fractional analogues of Hodge decomposition and higher order Poincare inequalities as well as several localization effects for nonlocal operators similar to the fractional laplacian are developed and applied.

some details added, some errors removed. new introduction

References in corpus (3)

• A Remark on Gauge Transformations and the Moving Frame Method
• 3-Commutators Estimates and the Regularity of 1/2 Harmonic Maps into Spheres
• Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains

Cited by in corpus (26)

• Sharp commutator estimates via harmonic extensions
• Nonlinear commutators for the fractional p-Laplacian and applications
• Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)
• ε-regularity for systems involving non-local, antisymmetric operators
• n/p-Harmonic maps: regularity for the sphere case
• Calderon-Zygmund type estimates for nonlocal PDE with Hölder continuous kernel
• On energy-critical half-wave maps into ${\mathbb{S}}^2$
• Integro-differential harmonic maps into spheres
• A Note on Regularity for the n-dimensional H-System assuming logarithmic higher Integrability
• Second variation of domain functionals and applications to problems with Robin boundary conditions
• On some knot energies involving Menger curvature
• Plateau's problem in Finsler 3-space
• Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains
• Free boundary minimal surfaces: a nonlocal approach
• On regularity theory for n/p-harmonic maps into manifolds
• Boundary regularity for conformally invariant variational problems with Neumann data
• Infinite time blow-up for half-harmonic map flow from $\mathbb{R}$ into ${\mathbb{S}}^1$
• Weak solutions of geometric flows associated to integro-differential harmonic maps
• Empirical Study of the 1-2-3 Trend Indicator
• Uniqueness and Regularity of the Fractional Harmonic Gradient Flow in $S^{n-1}$
• Compactness and Bubbles Analysis for 1/2-harmonic Maps
• Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions
• Minimal $W^{s,\frac{n}{s}}$-harmonic maps in homotopy classes
• Epsilon-regularity for p-harmonic maps at a free boundary on a sphere
• Comparing maximal mean values on different scales
• Non-degeneracy and quantitative stability of half-harmonic maps from $\mathbb{R}$ to $\mathbb{S}$