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THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN
Published online by Cambridge University Press: 02 September 2013
Abstract
In this paper we study the dependence of the first eigenvalue of the infinity Laplace with respect to the domain. We prove that this first eigenvalue is continuous under some weak convergence conditions which are fulfilled when a sequence of domains converges in Hausdorff distance. Moreover, it is Lipschitz continuous but not differentiable when we consider deformations obtained via a vector field. Our results are illustrated with simple examples.
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2013
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