Continuity of almost harmonic maps with the perturbation term in a critical space
type: Item
instance of: scholarly article
title: Continuity of almost harmonic maps with the perturbation term in a critical space
zbMATH Open document ID: 1504.58013
author: Mati ur Rahman
author: Yingshu Lü
author: Deliang Xu
published in: Chinese Annals of Mathematics. Series B
publication date: 2022-10-04T00:00:00Z
review text: The authors study the continuity estimate of the solutions of almost harmonic maps with the perturbation term \(f\) in a critical integrability class (Zygmund class) \(L^{\frac{n}{2}}\log^q L\), where \(n\) is the dimension, \(n\ge3\). It is shown that for \(q>\frac{n}{2}\), the solution must be continuous, and continuity modulus estimates can be provided. Finally, boundary continuity for the almost harmonic maps in high dimension is studied, as well.
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35S15
zbMATH DE Number: 7595968
zbMATH Keywords: almost harmonic maps
zbMATH Keywords: nonlinear elliptic PDE
zbMATH Keywords: boundary regularity
MaRDI profile type: Publication
full work available at URL: s11401-022-0347-0
OpenAlex ID: W4297922590
cites work: On the singular set of stationary harmonic maps
cites work: The boundary value problem for Dirac-harmonic maps
cites work: Partial regularity for stationary harmonic maps into spheres
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
cites work: Q3351775
cites work: Regularity of weakly harmonic maps from a surface into a manifold with symmetries
cites work: Fourth order approximation of harmonic maps from surfaces
cites work: Conservation Laws for Fourth Order Systems in Four Dimensions
cites work: SMALL ENERGY COMPACTNESS FOR APPROXIMATE HARMONIC MAPPINGS
cites work: Harmonic and quasi-harmonic spheres
cites work: Harmonic and quasi-harmonic spheres. II.
cites work: The problem of Plateau on a Riemannian manifold
cites work: Multiple integrals in the calculus of variations
cites work: Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps
cites work: A Trudinger type inequality for maps into a Riemannian manifold
cites work: An 𝐿^{𝑝} regularity theory for harmonic maps
cites work: Boundary regularity via Uhlenbeck–Rivière decomposition
cites work: A monotonicity formula for Yang-Mills fields
cites work: Conservation laws for conformally invariant variational problems
cites work: Partial regularity for harmonic maps and related problems
cites work: The existence of minimal immersions of 2-spheres
cites work: A regularity theory for harmonic maps
cites work: Higher integrability for solutions to a system of critical elliptic PDE
cites work: Decay estimates for Rivière's equation, with applications to regularity and compactness
cites work: On the evolution of harmonic maps in higher dimensions
cites work: Partial regularity for biharmonic maps, revisited
cites work: A new proof of regularity of weak solutions of the \(H\)-surface equation
cites work: Connections with \(L^ p \)bounds on curvature
cites work: Regularity of Dirac-Harmonic Maps
DOI: 10.1007/S11401-022-0347-0
description: scientific article; zbMATH DE number 7595968