Eigenvalue distribution of some fractal semi-elliptic differential operators

We consider differential operators of type Au(x) = u(x) + (-1)(t1) partial derivative (2t1) u(x)/partial derivativex(1)(2t1) + (-1)(t2) partial derivative (2t2)u(x)/partial derivativex(2)(2t2). x = (x(1),x(2)) is an element of R-2, and Sierpinski carpets Gamma subset of R-2. The aim of the paper is to investigate spectral properties of the fractal differential operator A(-1) circle tr(Gamma) acting in the anisotropic Sobolev space W-2((t1,t2)) (R-2) where tr(Gamma) is closely related to the trace operator tr(Gamma).