JournalszaaVol. 5, No. 6pp. 491–506

Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen

  • Matthias Günther

    Universität Leipzig, Germany
Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen cover

Abstract

The solvability of the nonlinear implicit equation F(u,f)=0F(u,f) = 0 in Banach spaces is examined. Theorem 1 covers situations in which DuF1D_uF^{-1} does not exist, but FF can be approximated by means of mappings FtF_t with better properties. Theorem 2 is of Moser-Nash type. In order to obtain optimal regularity results the Newton iteration method is combined with a triple approximation technique using smoothing operators and properties of certain interpolation spaces.

Cite this article

Matthias Günther, Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen. Z. Anal. Anwend. 5 (1986), no. 6, pp. 491–506

DOI 10.4171/ZAA/218