The normal form of the lincar elliptic systems of second order in Petrovskii sense with two variations and two unknow functions in divergence form is that Assume that the matrix -D(x) is positive definite and its least eigenvalueIn this paper we prove that if γ>0

then Dirichlet probfems of the elliptic systems in Petrovskii sense exist unigue. solutipn. Particularly

if Bi(x)=Ci(x) and D(x) is seminegative definite there is an unique solution