Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions
The spectral function Θ(t)=∑i=1∞exp(−tλj), where {λj}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 (∂∂ni+γi)u=0 on the pa...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000513 |
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| Summary: | The spectral function Θ(t)=∑i=1∞exp(−tλj), where {λj}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
(∂∂ni+γi)u=0 on the parts ∂Ωi(i=1,…,m) of the boundary ∂Ω can be considered, such that
∂Ω=∪i=1m∂Ωi, and γi(i=1,…,m) are assumed to be smooth functions which are not strictly positive. |
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| ISSN: | 0161-1712 1687-0425 |