An inequality à la Szegő–Weinberger for the p-Laplacian on convex sets-Reference-Cited by-同舟云学术

An inequality à la Szegő–Weinberger for the p-Laplacian on convex sets

Published:2016-09-14 Issue:06 Volume:18 Page:1550086
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Brasco Lorenzo¹,Nitsch Carlo²,Trombetti Cristina²

Affiliation:

1. Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 39 Rue Frédéric, Joliot Curie, 13453 Marseille, France

2. Dipartimento di Matematica e Applicazioni “R.Caccioppoli”, Complesso Universitario di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy

Abstract

In this paper, we prove a sharp upper bound for the first nontrivial eigenvalue of the [Formula: see text]-Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants and extensions are investigated as well.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199715500868

Reference20 articles.

1. Isoperimetric constants and some lower bounds for the eigenvalues of the P-laplacian

2. Sharp Estimates for Eigenfunctions of a Neumann Problem

3. Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

4. An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Role of Topology and Capacity in Some Bounds for Principal Frequencies;The Journal of Geometric Analysis;2024-07-29

2. Lyapunov-type inequalities for partial differential equations with -Laplacian;Forum Mathematicum;2021-01-19

3. Extremal p -Laplacian eigenvalues;Nonlinearity;2019-11-12

4. A toy Neumann analogue of the nodal line conjecture;Archiv der Mathematik;2017-12-07

5. On some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the p-Laplacian on a disk;Journal of Differential Equations;2017-08