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Über das Verhalten der Lösung des Dirichletproblems am Rand des Gebietes, wenn der Rand zur Klasse C2α gehört

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

In this paper the boundary behaviour of the solution of Dirichlet's problem for the equation Δu = f in domains with C2,α-boundary is studied. Without using Schauder's a priori estimates, we prove the following theorem, which is indispensable in Schauder's method to solve Dirichlet's problem for a general linear elliptic equation.

Theorem: Let (f, g)∈ C0,α (Ḡ)×C2,α (∂G) and u ∈ C0.0(Ḡ) ∩C2,α(G) be a solution of the problem Δu = f, u|∂G = g. Then u ∈ C2,α(Ḡ).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 163 - 176
Copyright
Copyright © Royal Society of Edinburgh 1978

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