Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure

Details Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure

2011-08-12

arxiv.org/abs/1108.2539v2

Mathematics

Analysis of PDEs

This paper has been withdrawn, since it has been accepted and the copyright has been assigned to the publisher

Scientific paper

We study Dirichlet problems for harmonic maps from a Riemannian $m$-manifold $(M,g)$ into a Finsler $n$-manifold $(N, F)$. We assume that the dimension of the source manifold $M$ is less than or equal to 4, and that the finsler structure $F(u,X)$ is given as F(u,X)= \sqrt{h_{ij}(u)X^i X^j + {\cal B}(u,X)}, (u\in N, X \in T_uN) where $(h_{ij})$ is a Riemannian metric and ${\cal B}(u,X)$ is a function on $TN$ with positive homogeneity of degree 2 with respect to $X$. Under these assumptions, an existence and interior regularity result will be given.

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