Bubbling phenomena of Palais-Smale-like sequences of \(m\)-harmonic type systems
type: Item
instance of: scholarly article
title: Bubbling phenomena of Palais-Smale-like sequences of \(m\)-harmonic type systems
zbMATH Open document ID: 0853.35036
DOI: 10.1007/BF01190823
author: Libin Mou
author: Changyou Wang
published in: Calculus of Variations and Partial Differential Equations
publication date: 1997-01-05T00:00:00Z
review text: The Palais-Smale condition for a functional \(E\) is a natural assumption for the existence of a critical point of \(E\). In many interesting cases the Palais-Smale condition fails due to the phenomena called bubbling. This failure of strong convergence is due to the loss of energy. Using a renormalization procedure to construct bubbles the authors describe in their main theorem the convergence behaviour of certain weakly convergent sequences and account for all the energy loss with a finite number of bubbles. Then they apply their result to \(m\)-harmonic maps to a Riemannian homogeneous space and to \(m\)-harmonic maps with a constant volume.
reviewed by: Alfred Göpfert
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 58E20
zbMATH DE Number: 898031
zbMATH Keywords: renormalization
zbMATH Keywords: weakly convergent sequences
zbMATH Keywords: homogeneous space
zbMATH Keywords: \(m\)-harmonic maps
MaRDI profile type: Publication
cites work: Convergence of solutions of H-systems or how to blow bubbles
cites work: Multiple solutions ofH-systems and Rellich's conjecture
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Compensated compactness and Hardy spaces
cites work: Direct methods in the calculus of variations
cites work: Partial regularity for stationary harmonic maps into spheres
cites work: Q5187597
cites work: Q3998311
cites work: Applications harmoniques de surfaces riemanniennes
cites work: Q5518064
cites work: Regularity for \(n\)-harmonic maps
cites work: Bubble tree convergence for harmonic maps
cites work: Large H-surfaces via the mountain-pass-lemma
cites work: A primer on hardy spaces, and some remarks on a theorem of evans and müller
cites work: A regularity theory for harmonic maps
cites work: The existence of minimal immersions of 2-spheres
cites work: Compactness properties of weakly p-harmonic maps into homogeneous spaces
cites work: Regularity for a class of nonlinear elliptic systems
cites work: An existence theorem for surfaces of constant mean curvature
cites work: Large solutions to the volume constrained Plateau problem
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description: scientific article; zbMATH DE number 898031