# A Non-Differentiability Result for the Inversion Operator between Sobolev Spaces

### G. Farkas

Technical University of Budapest, Hungary### Barnabas M. Garay

Technical University of Budapest, Hungary

## Abstract

The order of differentiability of the inversion operator $\mathcal J$ between certain spaces or manifolds of distributionally differentiable functions is shown to be sharp in the following sense. Up to a certain order $k$ guaranted by inverse function arguments, the operator $\mathcal J$ is everywhere differentiable and$\mathcal J^{(k)}$ is continuous. On the other hand, $\mathcal J$ is nowhere $k+1$ 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. 639–654

DOI 10.4171/ZAA/972