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Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth

Published online by Cambridge University Press:  15 August 2002

Bruno Nazaret
Bruno Nazaret*
Affiliation:
ENS Cachan, Antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France. Université de Cergy-Pontoise, Département de Mathématiques, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise, France.
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Abstract

This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the p-Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually, we end the paper by giving some analoguous results in the case where the datas present symmetries.

Keywords

Variational problemsnonlinear elliptic PDEoptimal Sobolev inequalitiesbest constant problemsp-Laplacian operator.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 559 - 575
Copyright
© EDP Sciences, SMAI, 1999

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