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Eine kritische Bemerkung zu Darstellungen der Schauderschen Beweistechnik für elliptische lineare Differentialgleichungen

Published online by Cambridge University Press:  14 November 2011

Manfred König
Manfred König
Affiliation:
Edelweiss Strasse 11, 8131 Berg-4-Höhenrain, Germany
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Synopsis

The object of this paper is to demonstrate, that with the open mapplng theorem of S.Banach one can prove very easily the following estimate

for all u ∈ C2,α and 0 ≤ t ≤ 1, if one knows, that for all bounded G ⊂ Rn, with boundary ∂G ∈ C2,α and for all (f, g) ∈ C0,α × C2,α (∂G) Dirichle's problem Δu = f, u|∂G = g has a solution u ∈ C2,α. This estimate can be used to solve Dirichle's problem for a general linear elliptic equation by Schauder's method.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 3-4 , 1978 , pp. 177 - 182
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

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