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Singularly perturbed spectral problems with Neumann boundary conditions

Permanent link
https://hdl.handle.net/10037/10901
DOI
https://doi.org/10.1080/17476933.2015.1076396
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Date
2015-09-07
Type
Peer reviewed
Journal article
Tidsskriftsartikkel

Author
Piatnitski, Andrey; Rybalko, A; Rybalko, V
Abstract
The paper deals with the Neumann spectral problem for a singularly perturbed second-order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue and eigenfunction. Using the logarithmic transformation, we reduce the studied problem to an additive eigenvalue problem for a singularly perturbed Hamilton–Jacobi equation. Then assuming that the Aubry set of the Hamiltonian consists of a finite number of points or limit cycles situated in the domain or on its boundary, we find the limit of the eigenvalue and formulate the selection criterion that allows us to choose a solution of the limit Hamilton–Jacobi equation which gives the logarithmic asymptotics of the principal eigenfunction
Description
Link to publishers version: 10.1080/17476933.2015.1076396
Citation
Piatnitski A, Rybalko A, Rybalko. Singularly perturbed spectral problems with Neumann boundary conditions. Complex Variables and Elliptic Equations. 2015;61(2):252-274
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