Three-term commutator estimates and the regularity of \(^{1}/_{2}\)-harmonic maps into spheres (Q638839)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Three-term commutator estimates and the regularity of \(^{1}/_{2}\)-harmonic maps into spheres |
scientific article; zbMATH DE number 5947665
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Three-term commutator estimates and the regularity of \(^{1}/_{2}\)-harmonic maps into spheres |
scientific article; zbMATH DE number 5947665 |
Statements
Three-term commutator estimates and the regularity of \(^{1}/_{2}\)-harmonic maps into spheres (English)
0 references
15 September 2011
0 references
Recently, the second author introduced a general formalism to prove the regularity of solutions to conformally invariant variational problems [Invent. Math. 168, No. 1, 1--22 (2007; Zbl 1128.58010)]. In the paper under review, the authors apply this point of view to 1/2-harmonic maps into spheres. More precisely, they define the energy \[ L(u)=\int_{\mathbb R} |\Delta^{1/4}u|^2\,dx \] and prove the following result: Any weak 1/2-harmonic map \(u\in H^{1/2}({\mathbb R},{\mathbb S}^{m-1})\) is in \(C^\infty\).
0 references
harmonic map
0 references
nonlinear elliptic PDE
0 references
regularity of solutions
0 references
commutator estimates
0 references
conformally invariant variational problems
0 references
