Assume that Ω is a domain in the complex plane C and A(z) is symmetric 2×2 matrix function with measurable entries, det A = 1 and such that 1/K|ξ| 2 ≤ ⟨A(z)ξ, ξ⟩ ≤ K|ξ| 2 , ξ ∈ R 2 , 1 ≤ K < ∞. In particular, for semi-linear elliptic equations of the form div (A(z)∇u(z)) = f (u(z)) in Ω we prove Factorization Theorem that says that every weak solution u to the above equation can be expressed as the composition u = T • ω, where ω : Ω → G stands for a K−quasiconformal homeomorphism generated by the matrix function A(z) and T (w) is a weak solution of the semi-linear equation △T (w) = J(w)f (T (w)) in G. Here the weight J(w) is the Jacobian of the inverse mapping ω −1 . Similar results hold for the corresponding nonlinear parabolic and hyperbolic equations. Some applications of these results in anisotropic media are given.

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