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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Chung Ling Yu
Journal: Trans. Amer. Math. Soc. 185 (1973), 429-443
MSC: Primary 35J45
MathSciNet review: 0326162
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Abstract: 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) $ \partial u/\partial x - \partial v/\partial y = au + bv + f,\partial u/\partial y + \partial v/\partial x = cu + dv + g$. The following areas will be investigated:

(1) the integral respresentations for solutions of (M) to the boundary $ \partial G$ 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).

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Keywords: First order elliptic equations, pseudo-analytic functions, Cauchy-Riemann equations, Cauchy problem, analytic continuation, Volterra integral equations
Article copyright: © Copyright 1973 American Mathematical Society