Navarro Climent, José Carlos, Rossi, Julio D., San Antolín Gil, Ángel, Saintier, Nicolas
The dependence of the first eigenvalue of the infinity Laplacian with respect to the domain
Glasgow Mathematical Journal. 2014, 56(2): 241-249. doi:10.1017/S0017089513000219
URI: http://hdl.handle.net/10045/36560
DOI: 10.1017/S0017089513000219
ISSN: 0017-0895 (Print)
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.
Keywords:Nonlinear elliptic equations, Eigenvalues
Cambridge University Press
info:eu-repo/semantics/article