Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains

We study spectral estimates of the divergence form uniform elliptic operators −div[A(z)∇f(z)] with the Dirichlet boundary condition in bounded non-Lipschitz simply connected domains Ω ⊂ C. The suggested method is based on the quasiconformal composition operators on Sobolev spaces with applications to the weighted Poincaré-Sobolev inequalities.