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The Hilbert boundary value problem for nonlinear elliptic systems

Published online by Cambridge University Press:  14 November 2011

Heinrich Begehr  and
George C. Hsiao
Heinrich Begehr
Affiliation:
Freie Universität Berlin, I. Mathematisches Institut, Hüttenweg 9, 1000 Berlin 33, Germany
George C. Hsiao
Affiliation:
Department of Mathematics, University of Delaware, 501 Kirkbridge Office Building, Newark, Delaware 19711, U.S.A.
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Synopsis

The Hilbert boundary value problem for a first order nonlinear elliptic system in the plane with linear boundary conditions of nonnegative index is (under suitable side conditions uniquely) solved by use of the Newton imbedding method. This constructive method is based on an a priori estimate which arises from an integral representation formula for C1-functions first developed by Haack and Wendland. The approximation procedure yields an error estimate too.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 97 - 112
Copyright
Copyright © Royal Society of Edinburgh 1983

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