On the perturbation of eigenvalues for the p-Laplacian

In this Note the differentiability with respect to the domain of the first Dirichlet eigenvalue of the minus p-laplacian is shown for the first time. An explicit formula for the first variation is obtained. The proof, based on the variational formulation and C1-alpha-type estimates, even simplifies the corresponding to the linear case p = 2. An application to the profile behaviour of positive solutions to a class of logistic problems is given. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.