  We study unitary minimal models coupled to Liouville gravity using Douglas
string equation. Our approach is based on the assumption that there exist an
appropriate solution of the Douglas string equation and some special choice of
the resonance transformation such that necessary selection rules of the minimal
Liouville gravity are satisfied. We use the connection with the Frobenius
manifold structure. We argue that the flat coordinates on the Frobenius
manifold are the most appropriate choice for calculating correlation functions.
We find the appropriate solution of the Douglas string equation and show that
it has simple form in the flat coordinates. Important information is encoded in
the structure constants of the Frobenius algebra. We derive these structure
constants in the canonical coordinates and in the physically relevant domain in
the flat coordinates. We find the leading terms of the resonance transformation
and express the coefficients of the resonance transformation in terms of Jacobi
polynomials.
