THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN
J. C. NAVARRO, Julio Daniel Rossi, Á. San Antolín, Nicolas Saintier · Glasgow Mathematical Journal · 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.