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...

Descripción completa

Detalles Bibliográficos
Autores principales: Navarro, J.C., Rossi, J.D., San Antolin, A., Saintier, N.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00170895_v56_n2_p241_Navarro
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00170895_v56_n2_p241_Navarro
record_format dspace
spelling todo:paper_00170895_v56_n2_p241_Navarro2023-10-03T14:14:57Z The dependence of the first eigenvalue of the infinity laplacian with respect to the domain Navarro, J.C. Rossi, J.D. San Antolin, A. Saintier, N. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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.
format JOUR
author Navarro, J.C.
Rossi, J.D.
San Antolin, A.
Saintier, N.
spellingShingle Navarro, J.C.
Rossi, J.D.
San Antolin, A.
Saintier, N.
The dependence of the first eigenvalue of the infinity laplacian with respect to the domain
author_facet Navarro, J.C.
Rossi, J.D.
San Antolin, A.
Saintier, N.
author_sort Navarro, J.C.
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
url http://hdl.handle.net/20.500.12110/paper_00170895_v56_n2_p241_Navarro
work_keys_str_mv AT navarrojc thedependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT rossijd thedependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT sanantolina thedependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT saintiern thedependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT navarrojc dependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT rossijd dependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT sanantolina dependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
AT saintiern dependenceofthefirsteigenvalueoftheinfinitylaplacianwithrespecttothedomain
_version_ 1807315059843530752

Ejemplares similares