One problem of conjugation of analytic functions in affinely transformed domains with piecewise smooth boundaries (Q1603053)

According the assertion of the author the series of problems of the mechanics of anisotropic continuous medium is reduced to the problem of conjugation of analytic functions in composed domains. In the present paper the author considers the problem of conjugation of analytic functions, satisfying given conditions on a piecewise smooth boundary of an affinely transformed composed domain. Depending on the existence of the roots of the characteristic equation produced through the coefficients, belonging to the interval \((0,1)\) the existence of the solution of the original problem has been proved.