This paper contains theorems of continuity and of $r$-th order Fr\'echet differentiability, with $r\geq 1$, for the autonomous composition operator in Sobolev spaces and an `inverse result', which shows the optimality of the continuity and differentiability theorems obtained.
Differentiability properties of the autonomous composition operator in Sobolev spaces.
LANZA DE CRISTOFORIS, MASSIMO
1997
Abstract
This paper contains theorems of continuity and of $r$-th order Fr\'echet differentiability, with $r\geq 1$, for the autonomous composition operator in Sobolev spaces and an `inverse result', which shows the optimality of the continuity and differentiability theorems obtained.
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