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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Autor principal: Rossi, Julio Daniel
Publicado: 2016
Materias:
Eigenvalue problems
First variations
Infinity Laplacian
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi
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 paper:paper_03621588_v42_n2_p613_Rossi2025-07-30T18:12:09Z On the first nontrivial eigenvalue of the ∞-laplacian with neumann boundary conditions Rossi, Julio Daniel 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. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi 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, Julio Daniel
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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
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
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03621588_v42_n2_p613_Rossi
http://hdl.handle.net/20.500.12110/paper_03621588_v42_n2_p613_Rossi
work_keys_str_mv AT rossijuliodaniel onthefirstnontrivialeigenvalueofthelaplacianwithneumannboundaryconditions
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