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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 3, 2000, pp. 639–654
DOI: 10.4171/ZAA/972

Published online: 2000-09-30

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

G. Farkas[1] and Barnabas M. Garay[2]

(1) Technical University of Budapest, Hungary
(2) Technical University of Budapest, Hungary

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.

Keywords: Inversion operators, differentiability, Sobolev spaces and manifolds

Farkas G., Garay Barnabas: A Non-Differentiability Result for the Inversion Operator between Sobolev Spaces. Z. Anal. Anwend. 19 (2000), 639-654. doi: 10.4171/ZAA/972