Calculus of Variations and Geometric Measure Theory
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L. Esposito - P. Roy - F. Sk

On the asymptotic behavior of the eigenvalues of nonlinear elliptic problems in domains becoming unbounded

created by sk on 21 Nov 2021
modified on 22 Nov 2021

[BibTeX]

Published Paper

Inserted: 21 nov 2021
Last Updated: 22 nov 2021

Journal: Asymptotic Analysis
Year: 2019
Doi: https://doi.org/10.3233/ASY-201626

ArXiv: 1911.08738 PDF

Abstract:

We analyze the asymptotic behavior of the eigenvalues of nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) boundary conditions on domains becoming unbounded. We make intensive use of Picone identity to overcome nonlinearity complications. Altogether the use of Picone identity makes the proof easier with respect to the known proof in the linear case. Surprisingly the asymptotic behavior under mixed boundary conditions critically differs from the case of pure Dirichlet boundary conditions for some class of problems.

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