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On the principal eigenvalue of a Robin problem with a large parameter. (English) Zbl 1136.35060

Summary: We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

MSC:

35P15 Estimates of eigenvalues in context of PDEs
35P05 General topics in linear spectral theory for PDEs
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References:

[1] and , Elliptic Partial Differential Equations of Second Order (Springer, Berlin, 1983).
[2] Lacey, Rocky Mountain J. Math. 26 pp 195– (1996)
[3] Lacey, SIAM J. Appl. Math. 58 pp 1622– (1998)
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