Comptes Rendus
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]
Ana-Maria Matei1
1 McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada
Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 255-258

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).

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).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02464-0

Ana-Maria Matei 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}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {255--258},
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Ana-Maria Matei. The effect of perturbations on the first eigenvalue of the $ \mathbf{p}$-Laplacian. Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 255-258. doi: 10.1016/S1631-073X(02)02464-0

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[2] J.P. Garzia Azorero; I. Peral Alonso Existence and nonuniqueness for the p-Laplacian eigenvalues, Comm. Partial Differential Equations, Volume 12 (1987), pp. 1389-1430

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

[4] L. Veron Some existence and uniqueness results for solution of some quasilinear elliptic equations on compact riemannian manifolds, Colloq. Math. Soc. Janos Bolyai, Volume 62 (1991), pp. 317-352

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