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March/April 2015 $L^p$-gradient harmonic maps into spheres and SO(N)
Armin Schikorra
Differential Integral Equations 28(3/4): 383-408 (March/April 2015).

Abstract

We consider critical points of the energy $$ E(v) := \int_{\mathbb R^n} |\nabla^s v|^{\frac{n}{s}}, $$ where $v$ maps locally into the sphere or $SO(N)$, and $\nabla^s = (\partial_1^s,\ldots,\partial_n^s)$ is the formal fractional gradient, i.e., $\partial_\alpha^s$ is a composition of the fractional Laplacian with the $\alpha$-th Riesz transform. We show that critical points of this energy are Hölder continuous. As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of $n$-harmonic maps into the sphere [22, 9], which is interesting on its own.

Citation

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Armin Schikorra. "$L^p$-gradient harmonic maps into spheres and SO(N)." Differential Integral Equations 28 (3/4) 383 - 408, March/April 2015.

Information

Published: March/April 2015
First available in Project Euclid: 4 February 2015

zbMATH: 1363.58010
MathSciNet: MR3306569

Subjects:
Primary: 35B65, 35J60, 35S05, 58E20

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 3/4 • March/April 2015
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