Comptes Rendus
no. 12
Partial Differential Equations
Anisotropic harmonic maps into homogeneous manifolds: a compactness result

Presented by: Pierre-Louis Lions

Mamadou Sango1
1 Department of Mathematics and Applied Mathematics, University of Pretoria/Mamelodi Campus, Pretoria 0002, South Africa
Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 923-926.

We introduce a new energy functional for maps between two manifolds, the critical points of which (p˜-harmonic maps) are solutions of a system of anisotropic quasilinear elliptic equations. In the case when the target is a homogeneous manifold with left invariant metric, we establish a compactness result for the corresponding p˜-harmonic maps. The proof relies on some deep results from harmonic analysis involving Hardy spaces.

Nous introduisons une nouvelle fonctionnelle d'énergie pour des applications sur des variétés ; les points critiques de cette fonctionnelle (applications p˜-harmoniques) sont solutions d'un système d'équations elliptique, quasilinéaire, anisotrope. Dans le cas où la variété cible est homogène et munie d'une métrique invariante à gauche, nous établissons un résultat de compacité pour les applications p˜-harmoniques correspondantes. La démonstration utilise un résultat fondamental d'analyse harmonique dans des espaces de Hardy.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.03.018

Mamadou Sango 1

1 Department of Mathematics and Applied Mathematics, University of Pretoria/Mamelodi Campus, Pretoria 0002, South Africa 
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Mamadou Sango. Anisotropic harmonic maps into homogeneous manifolds: a compactness result. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 923-926. doi : 10.1016/j.crma.2006.03.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.018/

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