Eine kritische Bemerkung zu Darstellungen der Schauderschen Beweistechnik für elliptische lineare Differentialgleichungen
Manfred König · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1978
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.