Weyl asymptotic formula for the Laplacian on domains with rough boundaries. (English) Zbl 1076.35085
The authors study asymptotic distribution of eigenvalues of the Laplacian on a bounded domain in \(\mathbb R^n\). They introduce a different technique which does not use an extension theorem. It allows to apply the Dirichlet-Neumann bracketing. They obtain the Weyl asymptotic formula with a remainder estimate for the Neumann Laplacian on domains without the extension property. The results are extended to a large class of domains and higher order operators. Other possible generalizations are discussed at the end.
Reviewer: Mohammed Bouchekif (Tlemcen)
MSC:
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 47F05 | General theory of partial differential operators |
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