A non-differentiablity result for the inversion operator between Sobolev spaces (Q5926107)

This article deals with the differentiability properties of the inverse operator \({\mathcal F}^{-1}\) to the mapping \({\mathcal F}\in H^s({\mathcal M}_1, {\mathcal M}_2)\) between compact \(C^\infty\)-manifolds \({\mathcal M}_1\) and \({\mathcal M}_2\). It is well-known that the operator NEWLINE\[NEWLINE{\mathcal F}^{-1}: {\mathcal D}^{s+k} ({\mathcal M}) \to H^s({\mathcal M},{\mathcal M})NEWLINE\]NEWLINE is of class \(C^k\) for any \(k\in\mathbb{N}\); the authors prove that this operator is nowhere \(k+1\) times differentiable if \(s,k \in\mathbb{N}\) and \(s> {k\over 2}+2\).