Compactness and bubble analysis for 1/2-harmonic maps

DOI10.1016/j.anihpc.2013.11.003zbMath1310.58011arXiv1210.2653OpenAlexW2963701315MaRDI QIDQ2259433

Francesca Da Lio

Publication date: 4 March 2015

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2653

zbMATH Keywords

regularity of solutionscommutator estimatesfractional harmonic mapsnonlinear elliptic PDE's

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Harmonic maps, etc. (58E20) Variational methods for second-order elliptic equations (35J20) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items (16)

Nonlinear commutators for the fractional \(p\)-Laplacian and applications ⋮ A fractional version of Rivière's \(\mathrm{GL(n)}\)-gauge ⋮ On energy-critical half-wave maps into \(\mathbb {S}^2\) ⋮ On regularity theory for \(n/p\)-harmonic maps into manifolds ⋮ Blow-up behavior of a fractional Adams–Moser–Trudinger-type inequality in odd dimension ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ Half-harmonic gradient flow: aspects of a non-local geometric PDE ⋮ Non-degeneracy and quantitative stability of half-harmonic maps from \(\mathbb{R}\) to \(\mathbb{S}\) ⋮ Epsilon-regularity for \(p\)-harmonic maps at a free boundary on a sphere ⋮ Regularity and quantification for harmonic maps with free boundary ⋮ Boundary equations and regularity theory for geometric variational systems with Neumann data ⋮ Nondegeneracy of half-harmonic maps from ℝ into 𝕊¹ ⋮ Minimizing \(1/2\)-harmonic maps into spheres ⋮ Problem analysis according to invariants ⋮ Partial regularity for fractional harmonic maps into spheres ⋮ Energy minimisers of prescribed winding number in an \(\mathbb{S}^1\)-valued nonlocal Allen-Cahn type model

Cites Work

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• Three-term commutator estimates and the regularity of \(^{1}/_{2}\)-harmonic maps into spheres
• Regularity of \(n/2\)-harmonic maps into spheres
• Complete Willmore surfaces in \(\mathbb{H}^3\) with bounded energy: boundary regularity and bubbling
• Factorization theorems for Hardy spaces in several variables
• An existence theorem for surfaces of constant mean curvature
• Modern Fourier Analysis
• A Quantization Property for Moving Line Vortices
• Energy quantization for biharmonic maps
• Function theory
• \(\varepsilon\)-regularity for systems involving non-local, antisymmetric operators

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