Convergence of minimizers for the \(p\)-Dirichlet integral
type: Item
instance of: scholarly article
title: Convergence of minimizers for the \(p\)-Dirichlet integral
zbMATH Open document ID: 0798.58022
DOI: 10.1007/BF03025730
author: Stephan Luckhaus
published in: Mathematische Zeitschrift
publication date: 1994-11-03T00:00:00Z
full work available at URL: https://eudml.org/doc/174538
review text: The introduction: The purpose of this paper is to show that a weakly convergent sequence of minimizing \(p\)-harmonic maps, \(\infty > p > 1\), between Riemannian manifolds converges to a minimizing \(p\)-harmonic map. For special target manifolds this has been proved by \textit{R. Hardt} and \textit{F. H. Lin} [Commun. Pure Appl. Math. 40, 555-588 (1987; Zbl 0646.49007), Theorem 6.4]; and if the domain is a ball, it has been proved by the author [Indiana Univ. Math. J. 37, No. 2, 349-368 (1988; Zbl 0641.58012)], and indeed used crucially in the blow up argument of that paper. The proof given here is a straightforward generalization of the latter method. The result is stated for more general functionals and problems with constraints, as it does not complicate the proof.
reviewed by: Andrea Ratto
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 49Q20
zbMATH DE Number: 561299
zbMATH Keywords: direct methods
zbMATH Keywords: minimizing \(p\)-harmonic maps
zbMATH Keywords: Riemannian manifolds
MaRDI profile type: Publication
cites work: Mappings minimizing theLp norm of the gradient
cites work: Q3782476
cites work: Homotopy classes in Sobolev spaces and the existence of energy minimizing maps
OpenAlex ID: W2055291032
description: scientific article; zbMATH DE number 561299