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22.—Analytic, Generalized, Hyperanalytic Function Theory and an Application to Elasticity*

Published online by Cambridge University Press:  14 February 2012

Robert P. Gilbert  and
Wolfgang L. Wendland
Robert P. Gilbert
Affiliation:
University of Delaware, and Freie Universität, Berlin
Wolfgang L. Wendland
Affiliation:
Technische Hochschule, Darmstadt.
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Synopsis

Though it is still an open problem for which class of first-order elliptic systems Carleman's theorem holds, this is proven here for a certain class of systems (with analytic coefficients) for which Douglis introduced the hypercomplex algebra and hyperanalytic functions. The proof is based on a representation formula generalising Vekua's approach with Volterra integral equations in C2 to more than two unknowns. The representation formula is of its own interest because it provides the generation of complete families of solutions. The equations of plane inhomogeneous elasticity problems lead to a system of the desired class.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 317 - 331
Copyright
Copyright © Royal Society of Edinburgh 1975

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