Eigenvalue distribution of some fractal semi-elliptic differential operators: Combinatorial approach

We obtain the sharp order of growth of the eigenvalue distribution function for the operator in the anisotropic Sobolev space H-t1,H-t2(Q), generated by the quadratic form integral (Q) \u \ (2)d mu, where Q subset of R-2 is the unit square and mu is a probability self-affine fractal measure on Q. The geometry of Supp mu should be in a certain way consistent with the parameters t(1), t(2).