no. 3
The effect of perturbations on the first eigenvalue of the 𝐩-Laplacian
[L'éffet des pérturbations sur la première valeur propre du 𝐩-Laplacien]
Matei, Ana-Maria1
1 McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada
Comptes Rendus. Mathématique, Tome 335 (2002) no. 3, pp. 255-258.

Soit Ω un domaine à bord Lipschitz d'une variété riemannienne compacte (M,g) et p>1. Nous montrons qu'on peut rendre le volume de M arbitrairement proche du volume de (Ω,g) tout en gardant la première valeur propre du p-Laplacien sur M uniformement minorée en termes de la première valeur propre du problème de Neumann pour le p-Laplacien sur (Ω,g).

Let Ω be a domain with Lipschitzian boundary of a compact Riemannian manifold (M,g) and p>1. We prove that we can make the volume of M arbitrarily close to the volume of (Ω,g) while the first eigenvalue of the p-Laplacian on M remains uniformly bounded from below in terms of the the first eigenvalue of the Neumann problem for the p-Laplacian on (Ω,g).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02464-0
Matei, Ana-Maria 1

1 McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada 
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     title = {The effect of perturbations on the first eigenvalue of the $ \mathbf{p}${-Laplacian}},
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Matei, Ana-Maria. The effect of perturbations on the first eigenvalue of the $ \mathbf{p}$-Laplacian. Comptes Rendus. Mathématique, Tome 335 (2002) no. 3, pp. 255-258. doi : 10.1016/S1631-073X(02)02464-0. http://www.numdam.org/articles/10.1016/S1631-073X(02)02464-0/

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[3] Tolksdorf, P. Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, Volume 51 (1984), pp. 126-150

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