Zwei Versionen von verallgemeinerten Sätzen über implizite Funktionen

Abstract

The solvability of the nonlinear implicit equation $F(u,f)=0$ in Banach spaces is examined. Theorem 1 covers situations in which $D_u{F}^{-1}$ does not exist, but $F$ can be approximated by means of mappings $F_t$ 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.