Harmonic maps on domains with piecewise Lipschitz continuous metrics

Details Harmonic maps on domains with piecewise Lipschitz continuous metrics Harmonic maps on domains with piecewise Lipschitz continuous metrics

2011-08-22

arxiv.org/abs/1108.4298v1

Mathematics

Analysis of PDEs

24 pages

Scientific paper

For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(\Omega, g)$ 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 $C^{1,\alpha}$-regularity of harmonic maps from $(\Omega, g)$ manifolds that support convex distance functions.

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