Harmonic maps on domains with piecewise Lipschitz continuous metrics
Haigang Li, Changyou Wang · Pacific Journal of Mathematics · 2013
We study harmonic maps ( , g) → (N, h), where ⊂ ޒ 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 ޒ k .We prove the partial regularity of stationary harmonic maps, and the global Lipschitz and piecewise C 1,α -regularity of weakly harmonic maps from ( , g) to manifolds (N, h) that support convex distance square functions.