We prove various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded nonempty domains of . In particular, we obtain a ‘Faber–Krahn’ type inequality for these operators. The proofs use a new rearrangement technique.
On montre divers résultats d'optimisation pour la première valeur propre d'opérateurs elliptiques généraux du second ordre sous forme divergence avec condition au bord de Dirichlet dans des domaines bornés non vides de classe de . En particulier, on obtient une inégalité de type « Faber–Krahn » pour ces opérateurs. Les preuves utilisent une nouvelle méthode de réarrangement.
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François Hamel 1; Nikolai Nadirashvili 2; Emmanuel Russ 1
@article{CRMATH_2007__344_3_169_0,
author = {Fran\c{c}ois Hamel and Nikolai Nadirashvili and Emmanuel Russ},
title = {Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form},
journal = {Comptes Rendus. Math\'ematique},
pages = {169--174},
publisher = {Elsevier},
volume = {344},
number = {3},
year = {2007},
doi = {10.1016/j.crma.2006.11.025},
language = {en},
}
TY - JOUR AU - François Hamel AU - Nikolai Nadirashvili AU - Emmanuel Russ TI - Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form JO - Comptes Rendus. Mathématique PY - 2007 SP - 169 EP - 174 VL - 344 IS - 3 PB - Elsevier DO - 10.1016/j.crma.2006.11.025 LA - en ID - CRMATH_2007__344_3_169_0 ER -
%0 Journal Article %A François Hamel %A Nikolai Nadirashvili %A Emmanuel Russ %T Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form %J Comptes Rendus. Mathématique %D 2007 %P 169-174 %V 344 %N 3 %I Elsevier %R 10.1016/j.crma.2006.11.025 %G en %F CRMATH_2007__344_3_169_0
François Hamel; Nikolai Nadirashvili; Emmanuel Russ. Some isoperimetric problems for the principal eigenvalues of second-order elliptic operators in divergence form. Comptes Rendus. Mathématique, Volume 344 (2007) no. 3, pp. 169-174. doi : 10.1016/j.crma.2006.11.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.025/
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