The dependence of the first eigenvalue of the infinity Laplacian with respect to the domain

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Title: The dependence of the first eigenvalue of the infinity Laplacian with respect to the domain
Authors: Navarro Climent, José Carlos | Rossi, Julio D. | San Antolín Gil, Ángel | Saintier, Nicolas
Research Group/s: Curvas Alpha-Densas. Análisis y Geometría Local
Center, Department or Service: Universidad de Alicante. Departamento de Análisis Matemático
Keywords: Nonlinear elliptic equations | Eigenvalues
Knowledge Area: Análisis Matemático
Issue Date: 2-Sep-2013
Publisher: Cambridge University Press
Citation: Glasgow Mathematical Journal. 2014, 56(2): 241-249. doi:10.1017/S0017089513000219
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.
Sponsor: Partially supported by MEC MTM2010-18128 (Spain).
URI: http://hdl.handle.net/10045/36560
ISSN: 0017-0895 (Print) | 1469-509X (Online)
DOI: 10.1017/S0017089513000219
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Glasgow Mathematical Journal Trust 2013
Peer Review: si
Publisher version: http://dx.doi.org/10.1017/S0017089513000219
Appears in Collections:INV - CADAGL - Artículos de Revistas

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