The basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible so $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be injective and a sufficient condition for $f$ to be bijective and so a global diffeomorphism onto $Y$. This last condition is also necessary in the particular case $X=Y=\R^n$. In these theorems the key role is played by nonnegative {\it auxiliary scalar coercive functions}. As far as I know the use of such auxiliary functions in these questions is new. We find some first corollaries.

Diffeomorphisms with Banach space domains

ZAMPIERI, Gaetano
1992-01-01

Abstract

The basic element is a $C^1$ mapping $f:X\to Y$, with $X,Y$ Banach spaces, and with derivative everywhere invertible so $f$ is a local diffeomorphism at every point. The aim of this paper is to find a sufficient condition for $f$ to be injective and a sufficient condition for $f$ to be bijective and so a global diffeomorphism onto $Y$. This last condition is also necessary in the particular case $X=Y=\R^n$. In these theorems the key role is played by nonnegative {\it auxiliary scalar coercive functions}. As far as I know the use of such auxiliary functions in these questions is new. We find some first corollaries.
1992
Local diffeomorphisms between Banach spaces, auxiliary scalar coercive functions, sufficient conditions for injectivity, sufficient conditions for bijectivity
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/393337
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