Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions

E. M. E. Zayed

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-6

Abstract:

The spectral function Θ ( t ) = ∑ i = 1 ∞ exp ( − t λ j ) , where { λ j } j = 1 ∞ are the eigenvalues of the negative Laplace-Beltrami operator − Δ , is studied for a compact Riemannian manifold Ω of dimension k with a smooth boundary ∂ Ω , where a finite number of piecewise impedance boundary conditions ( ∂ ∂ n i + γ i ) u = 0 on the parts ∂ Ω i ( i = 1 , … , m ) of the boundary ∂ Ω can be considered, such that ∂ Ω = ∪ i = 1 m ∂ Ω i , and γ i ( i = 1 , … , m ) are assumed to be smooth functions which are not strictly positive.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:921807

DOI: 10.1155/S0161171297000513

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