Nous introduisons une nouvelle fonctionnelle d'énergie pour des applications sur des variétés ; les points critiques de cette fonctionnelle (applications -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 -harmoniques correspondantes. La démonstration utilise un résultat fondamental d'analyse harmonique dans des espaces de Hardy.
We introduce a new energy functional for maps between two manifolds, the critical points of which (-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 -harmonic maps. The proof relies on some deep results from harmonic analysis involving Hardy spaces.
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@article{CRMATH_2006__342_12_923_0, author = {Sango, Mamadou}, title = {Anisotropic harmonic maps into homogeneous manifolds: a compactness result}, journal = {Comptes Rendus. Math\'ematique}, pages = {923--926}, publisher = {Elsevier}, volume = {342}, number = {12}, year = {2006}, doi = {10.1016/j.crma.2006.03.018}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.03.018/} }
TY - JOUR AU - Sango, Mamadou TI - Anisotropic harmonic maps into homogeneous manifolds: a compactness result JO - Comptes Rendus. Mathématique PY - 2006 SP - 923 EP - 926 VL - 342 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.03.018/ DO - 10.1016/j.crma.2006.03.018 LA - en ID - CRMATH_2006__342_12_923_0 ER -
%0 Journal Article %A Sango, Mamadou %T Anisotropic harmonic maps into homogeneous manifolds: a compactness result %J Comptes Rendus. Mathématique %D 2006 %P 923-926 %V 342 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2006.03.018/ %R 10.1016/j.crma.2006.03.018 %G en %F CRMATH_2006__342_12_923_0
Sango, Mamadou. Anisotropic harmonic maps into homogeneous manifolds: a compactness result. Comptes Rendus. Mathématique, Tome 342 (2006) no. 12, pp. 923-926. doi : 10.1016/j.crma.2006.03.018. http://archive.numdam.org/articles/10.1016/j.crma.2006.03.018/
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