[Sur les valuers propres et le problème de Dirichlet pour des opérateurs complètement non-linéaires]
On étudie des équations complètement non-linéaires, uniformément elliptiques, du type . On
- – montre que les opérateurs convexes et positivement homogènes de degré 1 possèdent deux valeurs propres et deux fonctions propres principales. On étudie les propriétés de ces objets ;
- – obtient des résultats d'existence et d'unicité pour des équations qui ne sont pas « propres », mais dont les valeurs propres (l'une ou les deux) sont positives ;
- – obtient un résultat d'existence pour une équation de Isaac.
We study uniformly elliptic fully nonlinear equations of the type . We
- – show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects;
- – obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive;
- – obtain an existence result for non-proper Isaac's equations.
Accepté le :
Publié le :
@article{CRMATH_2006__342_2_115_0,
author = {Quaas, Alexander and Sirakov, Boyan},
title = {On the principal eigenvalues and the {Dirichlet} problem for fully nonlinear operators},
journal = {Comptes Rendus. Math\'ematique},
pages = {115--118},
publisher = {Elsevier},
volume = {342},
number = {2},
year = {2006},
doi = {10.1016/j.crma.2005.11.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.11.003/}
}
TY - JOUR AU - Quaas, Alexander AU - Sirakov, Boyan TI - On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators JO - Comptes Rendus. Mathématique PY - 2006 SP - 115 EP - 118 VL - 342 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.11.003/ DO - 10.1016/j.crma.2005.11.003 LA - en ID - CRMATH_2006__342_2_115_0 ER -
%0 Journal Article %A Quaas, Alexander %A Sirakov, Boyan %T On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators %J Comptes Rendus. Mathématique %D 2006 %P 115-118 %V 342 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.11.003/ %R 10.1016/j.crma.2005.11.003 %G en %F CRMATH_2006__342_2_115_0
Quaas, Alexander; Sirakov, Boyan. On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators. Comptes Rendus. Mathématique, Tome 342 (2006) no. 2, pp. 115-118. doi : 10.1016/j.crma.2005.11.003. http://www.numdam.org/articles/10.1016/j.crma.2005.11.003/
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⁎ Supported by FONDECYT, Grant No. 1040794, and ECOS grant C02E08.
