Geodesic
Behaviour of the first eigenvalue of the $p$-Laplacian in a domain with a hole
M. Sango1
1 Department of Mathematics Vista University Private Bag X050 Vanderbijlpark 1900, South Africa
Colloquium Mathematicum, Tome 87 (2001) no. 1, pp. 103-111

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We investigate the behaviour of a sequence $\lambda _{s}$, $s=1,2,\dots, $ of eigenvalues of the Dirichlet problem for the $p$-Laplacian in the domains $% {\mit\Omega} _{s}$, $s=1,2,\dots, $ obtained by removing from a given domain ${\mit\Omega} $ a set $E_{s}$ whose diameter vanishes when $s\rightarrow \infty $. We estimate the deviation of $\lambda _{s}$ 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.
DOI : 10.4064/cm87-1-6
Keywords: investigate behaviour sequence lambda dots eigenvalues dirichlet problem p laplacian domains mit omega dots obtained removing given domain mit omega set whose diameter vanishes rightarrow infty estimate deviation lambda eigenvalue limit problem derivation results construct appropriate asymptotic expansion sequence solutions original eigenvalue problem

M. Sango 1

1 Department of Mathematics Vista University Private Bag X050 Vanderbijlpark 1900, South Africa 
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M. Sango. Behaviour of the first eigenvalue
of the $p$-Laplacian in a domain with a hole. Colloquium Mathematicum, Tome 87 (2001) no. 1, pp. 103-111. doi: 10.4064/cm87-1-6

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