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

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 L...

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Autor principal: Rossi, Julio Daniel
Publicado: 2014
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v56_n2_p241_Navarro
http://hdl.handle.net/20.500.12110/paper_00170895_v56_n2_p241_Navarro
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00170895_v56_n2_p241_Navarro
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spelling paper:paper_00170895_v56_n2_p241_Navarro2023-06-08T14:39:01Z The dependence of the first eigenvalue of the infinity laplacian with respect to the domain Rossi, Julio Daniel 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. © Glasgow Mathematical Journal Trust 2013. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v56_n2_p241_Navarro http://hdl.handle.net/20.500.12110/paper_00170895_v56_n2_p241_Navarro
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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. © Glasgow Mathematical Journal Trust 2013.
author Rossi, Julio Daniel
spellingShingle Rossi, Julio Daniel
The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
title_short The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
title_full The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
title_fullStr The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
title_full_unstemmed The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
title_sort dependence of the first eigenvalue of the infinity laplacian with respect to the domain
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00170895_v56_n2_p241_Navarro
http://hdl.handle.net/20.500.12110/paper_00170895_v56_n2_p241_Navarro
work_keys_str_mv AT rossijuliodaniel thedependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT rossijuliodaniel dependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
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