Hearing the shape of membranes: further results
The spectral function θ(t)=∑m=1∞exp(−tλm), t>0 where {λm}m=1∞ are the eigenvalues of the Laplacian in Rn, 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+γju=0 on Γj (or Sj), j=1,…,J where Γ...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000825 |
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| Summary: | The spectral function θ(t)=∑m=1∞exp(−tλm), t>0 where {λm}m=1∞ are the eigenvalues of the Laplacian in Rn, 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+γju=0 on Γj (or Sj), j=1,…,J where Γj and Sj, j=1,…,J are parts of the boundaries of these domains respectively, while γj, j=1,…,J are positive constants. |
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| ISSN: | 0161-1712 1687-0425 |