no. G7
Article de recherche - Equations aux dérivées partielles
Conservation law of harmonic mappings in supercritical dimensions
[Loi de conservation des applications harmoniques en dimensions surcritiques]
Guo, Chang-Yu1 ; Xiang, Chang-Lin2 
1Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, 266237, Qingdao and Frontiers Science Center for Nonlinear Expectations, Ministry of Education, P. R. China
2Three Gorges Mathematical Research Center, China Three Gorges University, 443002, Yichang, P. R. China
Comptes Rendus. Mathématique, Tome 362 (2024) no. G7, pp. 769-773

In this short note, we provide a partial extension of Rivière’s convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.

Dans cette courte note, nous fournissons une extension partielle de la loi de conservation obtenue par Rivière’s en dimensions supérieures, sous certaines conditions d’intégrabilité de Lorentz pour la matrice de connexion. Comme application, nous obtenons une loi de conservation pour les applications faiblement harmoniques autour de points réguliers en dimensions supercritiques.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.592
Classification : 58E20, 35J60

Guo, Chang-Yu  1   ; Xiang, Chang-Lin  2

1 Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, 266237, Qingdao and Frontiers Science Center for Nonlinear Expectations, Ministry of Education, P. R. China
2 Three Gorges Mathematical Research Center, China Three Gorges University, 443002, Yichang, P. R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Guo, Chang-Yu; Xiang, Chang-Lin. Conservation law of harmonic mappings in supercritical dimensions. Comptes Rendus. Mathématique, Tome 362 (2024) no. G7, pp. 769-773. doi: 10.5802/crmath.592

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