ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY

Jiong SUN

系统科学与复杂性(英文) ›› 2000, Vol. 13 ›› Issue (2) : 181-189.

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系统科学与复杂性(英文) ›› 2000, Vol. 13 ›› Issue (2) : 181-189.
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ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY

    Jiong SUN
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ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY

    Jiong SUN
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摘要

In this paper the eigenvalue problem of Laplacian was investigated. Using the estimation of entropy and approximation numbers of Sobolev embeddings, we obtained asymptotic formulae of its eigenvalue counting functions on an unbounded domain (finite measure)with a fractal boundary.

Abstract

In this paper the eigenvalue problem of Laplacian was investigated. Using the estimation of entropy and approximation numbers of Sobolev embeddings, we obtained asymptotic formulae of its eigenvalue counting functions on an unbounded domain (finite measure)with a fractal boundary.

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Asymptotic formulae / eigenvalue

Key words

Asymptotic formulae / eigenvalue / unbounded domain / fractal

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Jiong SUN. ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY. 系统科学与复杂性(英文), 2000, 13(2): 181-189
Jiong SUN. ON ASYMPTOTIC FORMULAE OF EIGENVALUE COUNTING FUNCTIONS OF LAPLACIAN ON AN UNBOUNDED DOMAIN WITH A FRACAL BOUNDARY. Journal of Systems Science and Complexity, 2000, 13(2): 181-189
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