Eigenvalue distribution of elliptic operators of second order with Neumannboundary conditions in a snowflake domain

Authors
Citation
G. Berger, Eigenvalue distribution of elliptic operators of second order with Neumannboundary conditions in a snowflake domain, MATH NACHR, 220, 2000, pp. 11-32
Citations number
16
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE NACHRICHTEN
ISSN journal
0025584X → ACNP
Volume
220
Year of publication
2000
Pages
11 - 32
Database
ISI
SICI code
0025-584X(2000)220:<11:EDOEOO>2.0.ZU;2-M
Abstract
Spectral properties of strongly elliptic operators of second order on bound ed snowflake domains without W-2(1)-extension property are investigated. We prove that the operators have a pure point spectrum and the asymptotic eig envalue distributions for the counting function N(lambda) are of Weyl type. It is shown that the remainder estimate of N(lambda) for Dirichlet and Neu mann boundary conditions depends on the inner and outer Minkowski dimension of the boundary partial derivative Omega, respectively.