Partial regularity for biharmonic maps, revisited
type: Item
instance of: scholarly article
title: Partial regularity for biharmonic maps, revisited
zbMATH Open document ID: 1151.58011
author: Michael Struwe
published in: Calculus of Variations and Partial Differential Equations
publication date: 2008-07-25T00:00:00Z
full work available at URL: http://hdl.handle.net/20.500.11850/3958
review text: Using gauge theory, the author gives a new proof for the partial regularity of stationary (extrinsically) biharmonic maps of domains in \(\mathbb R^m\), \(m>4\). The paper continues studies from [\textit{T. Rivière} and \textit{M. Struwe}, Commun. Pure Appl. Math. 61, 451--463 (2008; Zbl 1144.58011)] where harmonic maps are discussed. The critical \(m=4\) case has been considered in [\textit{T. Lamm} and \textit{T. Rivière}, Commun. Partial Differ. Equations 33, 245--262 (2008; Zbl 1139.35328)]. The proof is based on writing the nonlinearity in a way that allows the use of the Coulomb gauge theorems by Meyer and Rivière, Tao and Tian. Actually, this gives a new proof for the partial regularity that has been proven in [\textit{C. Wang}, Commun. Pure Appl. Math. 57, 419--444 (2004; Zbl 1055.58008)]. In an appendix, some details are given which may help clarify the previous proof.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35J35
zbMATH DE Number: 5304002
zbMATH Keywords: partial regularity
zbMATH Keywords: biharmonic maps
zbMATH Keywords: Morrey space
zbMATH Keywords: gauge theory
MaRDI profile type: Publication
OpenAlex ID: W1997779676
cites work: Composition Operators on Potential Spaces
cites work: A monotonicity formula for stationary biharmonic maps
cites work: Q4267561
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
cites work: Q4537523
cites work: A partial regularity result for a class of stationary Yang-Mills fields in high dimension.
cites work: Conservation laws for conformally invariant variational problems
cites work: Partial regularity for harmonic maps and related problems
cites work: On biharmonic maps and their generalizations
cites work: GAGLIARDO–NIRENBERG INEQUALITIES WITH A BMO TERM
cites work: A singularity removal theorem for Yang-Mills fields in higher dimensions
cites work: Connections with \(L^ p \)bounds on curvature
cites work: Stationary biharmonic maps fromRm into a Riemannian manifold
DOI: 10.1007/S00526-008-0175-4
description: scientific article; zbMATH DE number 5304002