Reflection principle for systems of first order elliptic equations with analytic coefficients

Author:
Chung Ling Yu

Journal:
Trans. Amer. Math. Soc. **164** (1972), 489-501

MSC:
Primary 30A92

DOI:
https://doi.org/10.1090/S0002-9947-1972-0293110-0

MathSciNet review:
0293110

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *T* be a simply connected domain of the plane, whose boundary contains a portion of the *x*-axis. Also let and be holomorphic functions for , with for for . Furthermore, we assume that and are real valued functions for . Our reflection principle states that for any solution of an equation of the type in *T* under the boundary condition on can be continued analytically across the *x*-axis, onto the entire mirror image .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0293110-0

Keywords:
Reflection principle,
first order elliptic equation,
pseudo-analytic functions,
Cauchy-Riemann equations

Article copyright:
© Copyright 1972
American Mathematical Society