Differential and Integral Equations

A nonlocal anisotropic eigenvalue problem

Gianpaolo Piscitelli

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Abstract

We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated \lq\lq twisted\rq\rq problem, we show that, this problem displays a saturation phenomenon: the first eigenvalue increases with the weight up to a critical value and then remains constant.

Article information

Source
Differential Integral Equations Volume 29, Number 11/12 (2016), 1001-1020.

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1476369326

Mathematical Reviews number (MathSciNet)
MR3557308

Zentralblatt MATH identifier
06674870

Subjects
Primary: 35P15: Estimation of eigenvalues, upper and lower bounds 49R50

Citation

Piscitelli, Gianpaolo. A nonlocal anisotropic eigenvalue problem. Differential Integral Equations 29 (2016), no. 11/12, 1001--1020. https://projecteuclid.org/euclid.die/1476369326.


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