Hearing the shape of membranes: further results

E. M. E. Zayed

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-8

Abstract:

The spectral function θ ( t ) = ∑ m = 1 ∞ exp ( − t λ m ) , t > 0 where { λ m } m = 1 ∞ are the eigenvalues of the Laplacian in R n , n = 2 or 3 , is studied for a variety of domains. Particular attention is given to circular and spherical domains with the impedance boundary conditions ∂ u ∂ r + γ j u = 0 on Γ j (or S j ), j = 1 , … , J where Γ j and S j , j = 1 , … , J are parts of the boundaries of these domains respectively, while γ j , j = 1 , … , J are positive constants.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:646870

DOI: 10.1155/S0161171290000825

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