Eigenvalue Distribution of Elliptic Operators of Second Order with Neumann Boundary Conditions in a Snowflake Domain

Spectral properties of strongly elliptic operators of second order on bounded snowflake domains without W¹₂–extension property are investigated. We prove that the operators have a pure point spectrum and the asymptotic eigenvalue distributions for the counting function N(λ) are of Weyl type. It is shown that the remainder estimate of N(λ) for Dirichlet and Neumann boundary conditions depends on the inner and outer Minkowski dimension of the boundary ∂Ω, respectively.