Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole

M. Sango. "Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole." Colloquium Mathematicae 87.1 (2001): 103-111. <http://eudml.org/doc/283423>.

@article{M2001,
abstract = {We investigate the behaviour of a sequence $λ_\{s\}$, s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains $Ω_\{s\}$, s = 1,2,..., obtained by removing from a given domain Ω a set $E_\{s\}$ whose diameter vanishes when s → ∞. We estimate the deviation of $λ_\{s\}$ from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.},
author = {M. Sango},
journal = {Colloquium Mathematicae},
keywords = {limit problem; asymptotic expansion},
language = {eng},
number = {1},
pages = {103-111},
title = {Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole},
url = {http://eudml.org/doc/283423},
volume = {87},
year = {2001},
}

TY - JOUR
AU - M. Sango
TI - Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole
JO - Colloquium Mathematicae
PY - 2001
VL - 87
IS - 1
SP - 103
EP - 111
AB - We investigate the behaviour of a sequence $λ_{s}$, s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains $Ω_{s}$, s = 1,2,..., obtained by removing from a given domain Ω a set $E_{s}$ whose diameter vanishes when s → ∞. We estimate the deviation of $λ_{s}$ from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.
LA - eng
KW - limit problem; asymptotic expansion
UR - http://eudml.org/doc/283423
ER -