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

DOI:
https://doi.org/10.1090/S0002-9947-1973-0326162-0

MathSciNet review:
0326162

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *a, b, c, d, f, g* be analytic functions of two real variables *x, y* in the plane. Consider the elliptic equation (M) . The following areas will be investigated:

(1) the integral respresentations for solutions of (M) to the boundary 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1973-0326162-0

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