THREE-TERM COMMUTATOR ESTIMATES AND THE REGULARITY OF 1/2-HARMONIC MAPS INTO SPHERES

被引：72

作者：

Da Lio, Francesca ^{[1
,2
]}

Riviere, Tristan ^{[2
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35121 Padua, Italy

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

ANALYSIS & PDE | 2011年 / 4卷 / 01期

关键词：

harmonic map; nonlinear elliptic PDE; regularity of solutions; commutator estimates; HARDY-SPACES;

D O I：

10.2140/apde.2011.4.149

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the regularity of weak 1/2-harmonic maps from the real line into a sphere. A key step is the formulation of the 1/2-harmonic map equation in the form of a nonlocal linear Schrodinger type equation with three-term commutators on the right-hand side. We then establish a sharp estimate for these three-term commutators.

引用

页码：149 / 190

页数：42

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