Differential and Integral Equations

Energy identity for $m$-harmonic maps

Changyou Wang and ShihShu Walter Wei

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Abstract

For $m\ge 3$, let $M$, with dimension $m$, and $N$ be compact Riemannian manifolds without boundaries. We prove the energy identity (1.2) for a sequence of weakly convergent $m$-harmonic maps in $C^1(M,N)$. We also generalize the result to certain regular approximated $m$-harmonic maps whose tension fields are bounded in $L^{m\over m-1}$.

Article information

Source
Differential Integral Equations, Volume 15, Number 12 (2002), 1519-1532.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060711

Mathematical Reviews number (MathSciNet)
MR1920259

Zentralblatt MATH identifier
1037.58011

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.

Citation

Wang, Changyou; Wei, ShihShu Walter. Energy identity for $m$-harmonic maps. Differential Integral Equations 15 (2002), no. 12, 1519--1532. https://projecteuclid.org/euclid.die/1356060711


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