Evolution of harmonic maps with Dirichlet boundary conditions
type: Item
instance of: scholarly article
title: Evolution of harmonic maps with Dirichlet boundary conditions
zbMATH Open document ID: 0845.35049
author: Yunmei Chen
author: Fanghua Lin
published in: Communications in Analysis and Geometry
publication date: 1996-09-11T00:00:00Z
review text: The global existence of weak flows of harmonic maps between two compact Riemannian manifolds with boundary \(M\) and \(N\) with Dirichlet boundary conditions is proved. This weak solution is smooth off a closed subset in \(\overline M\times \mathbb{R}_+\), which has a locally finite \(m\)-dimensional Hausdorff measure with respect to the parabolic metric. Moreover, as \(t\to +\infty\) suitably, the solution \(u(t)\) converges weakly in \(H^1(M, N)\) to a harmonic map \(u_\infty: M\to N\) with \(u_\infty|_{\partial M}= u_0|_{\partial M}\), which is smooth off a set in \(\overline M\), whose \((m- 2)\)-dimensional Hausdorff measure can be bounded in terms of the \(C^2\)-norm of \(u_0\) and the energy \(E(u_0)\).
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 836423
zbMATH Keywords: partial regularity
zbMATH Keywords: global existence
zbMATH Keywords: weak flows of harmonic maps
reviewed by: Yung Ming Chen
MaRDI profile type: Publication
DOI: 10.4310/CAG.1993.V1.N3.A1
description: scientific article; zbMATH DE number 836423