Irregular but nonfractal drums andn-dimensional weyl conjecture |
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Authors: | Hua Chen |
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Institution: | (1) Department of Mathematics, Wuhan University, 430072 Wuhan, People's Republic of China |
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Abstract: | In this paper, we study the asymptotics of the spectrum of the Dirichlet (or Neumann) Laplacian in a bounded open set R
n
(n 1) with irregular but nonfractal boundary![part](/content/p67826657l0552h7/xxlarge8706.gif) . We give a partial resolution of the Weyl conjecture, i.e. for the counting functionN
i
( )(i=0 : Dirichlet;i=1 : Neumann), we have got a precise estimate of the remainder term÷
i
( )= ( ) –N
i
( ) for large , where ( ) is the Weyl term. This implies that for the irregular but nonfractal drum , not only the volume | |
n
is spectral invariant but also the area of boundary |![part](/content/p67826657l0552h7/xxlarge8706.gif) |
n–1 might be spectral invariant as well.Partially supported by the National Natural Science Foundation of China and the Grant of Chinese State Education Committee. |
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Keywords: | |
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