Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure
type: Item
instance of: scholarly article
title: Existence and regularity of weakly harmonic maps into a Finsler manifold with a special structure
zbMATH Open document ID: 1268.58016
author: Atsushi Tachikawa
published in: Bulletin of the London Mathematical Society
publication date: 2012-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1108.2539
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 49N60
zbMATH DE Number: 6092632
zbMATH Keywords: Harmonic map
zbMATH Keywords: Finsler manifold
zbMATH Keywords: Euler-Lagrange equations
zbMATH Keywords: regularity problems
zbMATH Keywords: Riemannian metric
MaRDI profile type: Publication
OpenAlex ID: W2007978792
arXiv ID: 1108.2539
DOI: 10.1112/BLMS/BDS030
review text: 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.
reviewed by: Cornelia-Livia Bejan
description: scientific article; zbMATH DE number 6092632