Vol. 264, No. 1, 2013

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Harmonic maps on domains with piecewise Lipschitz continuous metrics

Haigang Li and Changyou Wang

Vol. 264 (2013), No. 1, 125–149

We study harmonic maps ,g) (N,h), where Ω n 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 k. We prove the partial regularity of stationary harmonic maps, and the global Lipschitz and piecewise C1-regularity of weakly harmonic maps from ,g) to manifolds (N,h) that support convex distance square functions.

piecewise continuous metric, harmonic map, regularity
Mathematical Subject Classification 2010
Primary: 35J50, 58E20
Received: 7 March 2012
Revised: 19 October 2012
Accepted: 6 May 2013
Published: 5 July 2013
Haigang Li
School of Mathematical Sciences and Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing Normal University
Beijing, 100875
Changyou Wang
Department of Mathematics
University of Kentucky
Lexington, KY 40506
United States