Existence for \(VT\)-harmonic maps from compact manifolds with boundary
In this paper, the authors prove an existence theorem for the solutions of the Dirichlet problem for a generalization of harmonnic maps, the so called \(VT\)-harmonic maps, defined on a compact differentiable manifold with boundary. \(VT\) harmonic maps were introduced by \textit{Q. Chen} et al. [Ann. Global Anal. Geom. 57, No. 1, 71--94 (2020; Zbl 1432.58010)] as a generalization of harmonic maps introducing a vector field \(V\) and a tensor field \(T\). The main result of the paper is stated in Theorem 1.5 of the paper and proves, under suitable assumptions, the existence of a \(VT\)-harmonic map satisfying some suitable boundary conditions.
scientific article; zbMATH DE number 7606691