Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces

摘要

We study the spectral properties of the compact non-negative self-adjoint operator T = A(-1) o tr(Gamma) acting in the anisotropic Sobolev space H-2(s,a)(R-n) and give two-sided estimates for the asymptotic behaviour of its eigenvalues lambda(k)(T), where A is a semi-elliptic differential operator of type Au(x) = (-1)s(1) partial derivative(2s1)u(x)/partial derivative x(1)(2s1)+...+(-1)(sn) partial derivative(2sn1)u(x)/partial derivative x(1)(2sn) + u(x), and tr(Gamma) a special trace operator on an anisotropic d-set Gamma.