Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure (Q2918793)

Let \((M,g)\) be a Riemannian manifold of dimension less than or equal to 4. Let \((N,F)\) be a Finsler manifold with the Finsler structure \(F(u,X)\) given by: \(F(u,X) = \sqrt{h_{ij}(u)X^iX^j + B(u,X)}, (u\in N, X\in T_uN)\), where \((h_{ij})\) is a Riemannian metric on \(N\) and \(B(u,X)\) is a function on \(TN\) with positive homogeneity of degree 2, with respect to \(X\). Dirichlet problems for harmonic maps from \(M\) to \(N\) are studied here. The author shows the existence and regularity problems for weakly harmonic maps defined as weak solutions of the Euler-Lagrange equations. A maximum principle and interior Hölder continuity for minimizer of energies are also given here.