On a method of solving boundary value problems for elliptic systems of second-order differential equations in the plane

In this work we describe a new method of solving boundary value problems for elliptic systems of second-order differential equations in the plane. The new method is illustrated for the case of an exterior Dirichlet problem for an elliptic system with constant coefficients. By means of this method we obtain an explicit form of the solution of exterior problems of Dirichlet and of Neumann, and we establish an effective method of solving more general boundary value problems for systems of differential equations with constant coefficients in domains which are bounded by an ellipse.
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