Comptes Rendus
no. 1
On one-homogeneous solutions to elliptic systems in two dimensions
[Sur les solutions un-homogènes des systèmes elliptiques en dimension deux]
Daniel Phillips1
1 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 39-42.

Dans cette Note, nous considérons une classe de systèmes d'équations elliptiques non linéaires du second ordre sous forme divergence à deux variables indépendantes. Nous prouvons que toutes les solutions faibles un-homogènes et Lipschitz continues sont linéaires.

In this Note we consider a class of nonlinear second order elliptic systems in divergence form and two independent variables. We prove that all Lipschitz continuous one-homogeneous weak solutions are linear.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02418-4

Daniel Phillips 1

1 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA 
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Daniel Phillips. On one-homogeneous solutions to elliptic systems in two dimensions. Comptes Rendus. Mathématique, Volume 335 (2002) no. 1, pp. 39-42. doi : 10.1016/S1631-073X(02)02418-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02418-4/

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[2] C.B. Morrey Existence and differentiability theorems for the solutions of variational problems for multiple integrals, Bull. Amer. Math. Soc., Volume 46 (1940), pp. 439-458

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