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Harmonic maps on
domains with piecewise Lipschitz continuous metrics
Haigang Li and Changyou Wang |
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Vol. 264 (2013), No. 1, 125–149
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Abstract |
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We study harmonic maps (Ω,g) → (N,h), where Ω ⊂ ℝn is a bounded domain divided into two pieces, the Riemannian metric g is Lipschitz in each piece, and (N,h) is a closed Riemannian submanifold of ℝk. We prove the partial regularity of stationary harmonic maps, and the global Lipschitz and piecewise C1,α-regularity of weakly harmonic maps from (Ω,g) to manifolds (N,h) that support convex distance square functions. |
Keywords
piecewise continuous metric, harmonic map, regularity
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Mathematical Subject Classification 2010
Primary: 35J50, 58E20
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Milestones
Received: 7 March 2012
Revised: 19 October 2012
Accepted: 6 May 2013
Published: 5 July 2013
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Authors |
| Haigang Li | |
| School of Mathematical Sciences and
Laboratory of Mathematics and Complex Systems, Ministry of
Education Beijing Normal University Beijing, 100875 China |
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| Changyou Wang | |
| Department of Mathematics University of Kentucky Lexington, KY 40506 United States |
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| http://www.ms.uky.edu/~cywang | |
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