A compactness theorem of n-harmonic maps
Changyou Wang
Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA
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Abstract
For , let be a bounded domain and be a compact smooth Riemannian submanifold without boundary. Suppose that are weak solutions to the (perturbed) -harmonic map equation (1.2), satisfying (1.3), and weakly in . Then is an -harmonic map. In particular, the space of -harmonic maps is sequentially compact for the weak- topology.
Résumé
Pour , soit un domaine borné et soit une sous-variété compacte sans bord. Soient des solutions de l'équation (perturbée) (1.2) pour les applications -harmoniques, telles que faiblement dans . Alors est une application -harmonique. En particulier, l'espace des applications -harmoniques est sequentiellement compact dans la topologie faible.
Cite this article
Changyou Wang, A compactness theorem of n-harmonic maps. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 4, pp. 509–519
DOI 10.1016/J.ANIHPC.2004.10.007