The order of differentiability of the inversion operator between certain spaces or manifolds of distributionally differentiable functions is shown to be sharp in the following sense. Up to a certain order guaranted by inverse function arguments, the operator is everywhere differentiable and is continuous. On the other hand, is nowhere times differentiable.
Cite this article
G. Farkas, Barnabas M. Garay, A Non-Differentiability Result for the Inversion Operator between Sobolev Spaces. Z. Anal. Anwend. 19 (2000), no. 3, pp. 639–654DOI 10.4171/ZAA/972