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Let a, b, c, d, f, g be analytic functions of two real variables x, y in the z = x + iy plane. Consider the elliptic equation (M) au/ax - av/ay = au + bv + f, au/ay + au/ax = cu + dv + g. The following areas will be investigated: (1) the integral respresentations for solutions of (M) to the boundary aG of a simply connected domain G; (2) reflection principles for (M) under nonlinear analytic boundary conditions; (3) the sufficient conditions for the nonexistence and analytic continuation for the solutions of the Cauchy problem for (M).

Cauchy problem and analytic continuation for systems of first order elliptic equations with analytic coefficients