In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IR<sup>n</sup>（n≥2） with non-smoot...In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IR<sup>n</sup>（n≥2） with non-smooth boundaryΩ and connected complement Ω<sub>e</sub>=IR<sup>n</sup>\.We can prove that if Ω satisfies a certain geometrical condition,then where φ（λ）=[（4π）<sup>n/2</sup>Γ(1+（n/2）]<sup>-1</sup>|Ω|<sub>n</sub>λ<sup>n/2</sup>,d<sub>n</sub>】0 depending only on n,and |·|<sub>j</sub>（j=n-1,n）is a j-dimensional Lebesgue measure.展开更多
基金Research partially supported by the Natural Science Foundation of Chinathe Grant of Chinese State Education Committee
文摘In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IR<sup>n</sup>（n≥2） with non-smooth boundaryΩ and connected complement Ω<sub>e</sub>=IR<sup>n</sup>\.We can prove that if Ω satisfies a certain geometrical condition,then where φ（λ）=[（4π）<sup>n/2</sup>Γ(1+（n/2）]<sup>-1</sup>|Ω|<sub>n</sub>λ<sup>n/2</sup>,d<sub>n</sub>】0 depending only on n,and |·|<sub>j</sub>（j=n-1,n）is a j-dimensional Lebesgue measure.
