Differential operators defining a solution of an elliptic-type equation

Abstract: We construct differential operators Kg(z), Lg(z), $$Kg(z),\;Lg(z),\,\,M\overline {f(z)} ,$$ , and $$N\overline {f(z)} $$ such that they map arbitrary holomorphic functions in a simply connected domain D in the complex plane z=x+iy into regular solutions of the equation <table><tbody><tr><td> $$W_{ \approx \bar \approx } + A(z,\bar z)W_{\bar \approx } + B(z,z)W = 0.$$ </td></tr></tbody></table> We give examples of applications of the constructed differential operators to a solution of the main boundary-value problems of mathematical physics. Bibliography: 1 title.