The Perron process applied to oblique derivative problems (Q1059776)

The author gives another proof of the solvability of the regular oblique derivative problem for a linear elliptic equation in Hölder spaces. The slight difference to chapter 6.7 of the well known monograph of \textit{D. Gilbarg} and \textit{N. S. Trudinger} [Elliptic partial differential equations of second order (1977; Zbl 0361.35003)] consists of the fact, that by using the same a-priori-estimates and a continuity method first a suitable defined local solvability is proved and second a solution is obtained by a Perron-process from local subsolution. - To my opinion in contrast to the claim this method does not seem to be more elementary than the treatment in the monograph cited above.