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arXiv · 1108.4298

Harmonic maps on domains with piecewise Lipschitz continuous metrics

Haigang Li·Changyou Wang
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Abstract

For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(Ω, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of stationary harmonic map and prove the partial regularity. We also discuss the global Lipschitz and piecewise $C^{1,α}$-regularity of harmonic maps from $(Ω, g)$ manifolds that support convex distance functions.

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Haigang Li, Changyou Wang. 2011-08-22. Harmonic maps on domains with piecewise Lipschitz continuous metrics. https://arxiv.org/abs/1108.4298

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