Weak limits of Palais-Smale sequences for a class of critical functionals
type: Item
instance of: scholarly article
title: Weak limits of Palais-Smale sequences for a class of critical functionals
zbMATH Open document ID: 0812.58018
DOI: 10.1007/BF01191297
author: Fabrice Béthuel
published in: Calculus of Variations and Partial Differential Equations
publication date: 1994-03-07T00:00:00Z
review text: Let \(F\) be a functional defined on a Hilbert space \(M\). The author states that in many interesting cases Palais-Smale sequences in \(M\) do not necessarily converge strongly to a critical point for \(F\). Therefore it is very important to prove that Palais-Smale sequences converge weakly to a critical point. Here the author studies the problem of surfaces of prescribed mean curvature and the related Palais-Smale sequences and extends the method to the harmonic map equation. For this purpose the author gives some preliminary results on isoperimetric inequality, Coarea formulas etc. followed by approximation theorem and a technique for computing boundary terms.
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 509959
zbMATH Keywords: harmonic map functional
zbMATH Keywords: Palais-Smale sequences
zbMATH Keywords: surfaces of prescribed mean curvature
reviewed by: R. N. Kaul
MaRDI profile type: Publication
cites work: On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
cites work: Multiple solutions ofH-systems and Rellich's conjecture
cites work: The approximation problem for Sobolev maps between two manifolds
cites work: Improved regularity of solutions to elliptic equations involving Jacobians and applications
cites work: Q4938956
cites work: Q4352757
cites work: On the plateau problem for surfaces of constant mean curvature
cites work: Q3351776
cites work: Q5518064
cites work: Convergence of surfaces of prescribed mean curvature
cites work: The existence of minimal immersions of 2-spheres
cites work: Boundary regularity and the Dirichlet problem for harmonic maps
cites work: Q3482498
cites work: Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme
cites work: The Dirichlet problem for the equation of prescribed mean curvature
cites work: Large solutions to the volume constrained Plateau problem
description: scientific article; zbMATH DE number 509959