On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions

We study the limit as p → ∞ of the first non-zero eigenvalue of the p-Laplacian with Neumann boundary conditions in a smooth bounded domain U We prove that = 2=diam(U), where diam(U) denotes the diameter of U with respect to the geodesic distance in U. We can think of as the first eigenvalue of the...

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Autores principales: Rossi, J.D., Saintier, N.
Formato: JOUR
Materias:
Eigenvalue problems
First variations
Infinity Laplacian
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03621588_v42_n2_p613_Rossi
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03621588_v42_n2_p613_Rossi2023-10-03T15:26:50Z On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions Rossi, J.D. Saintier, N. Eigenvalue problems First variations Infinity Laplacian We study the limit as p → ∞ of the first non-zero eigenvalue of the p-Laplacian with Neumann boundary conditions in a smooth bounded domain U We prove that = 2=diam(U), where diam(U) denotes the diameter of U with respect to the geodesic distance in U. We can think of as the first eigenvalue of the Laplacian with Neumann boundary conditions. We also study the regularity of as a function of the domain U proving that under a smooth perturbation Ut of U by diffeomorphisms close to the identity there holds that (U)+O(t). Although (Ut) is in general not differentiable at t = 0, we show that in some cases it is so with an explicit formula for the derivative. © 2016 University of Houston. 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_03621588_v42_n2_p613_Rossi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalue problems
First variations
Infinity Laplacian
spellingShingle Eigenvalue problems
First variations
Infinity Laplacian
Rossi, J.D.
Saintier, N.
On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
topic_facet Eigenvalue problems
First variations
Infinity Laplacian
description We study the limit as p → ∞ of the first non-zero eigenvalue of the p-Laplacian with Neumann boundary conditions in a smooth bounded domain U We prove that = 2=diam(U), where diam(U) denotes the diameter of U with respect to the geodesic distance in U. We can think of as the first eigenvalue of the Laplacian with Neumann boundary conditions. We also study the regularity of as a function of the domain U proving that under a smooth perturbation Ut of U by diffeomorphisms close to the identity there holds that (U)+O(t). Although (Ut) is in general not differentiable at t = 0, we show that in some cases it is so with an explicit formula for the derivative. © 2016 University of Houston.
format JOUR
author Rossi, J.D.
Saintier, N.
author_facet Rossi, J.D.
Saintier, N.
author_sort Rossi, J.D.
title On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
title_short On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
title_full On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
title_fullStr On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
title_full_unstemmed On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
title_sort on the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions
url http://hdl.handle.net/20.500.12110/paper_03621588_v42_n2_p613_Rossi
work_keys_str_mv AT rossijd onthefirstnontrivialeigenvalueofthelaplacianwithneumannboundaryconditions
AT saintiern onthefirstnontrivialeigenvalueofthelaplacianwithneumannboundaryconditions
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