JournalszaaVol. 19, No. 3pp. 639–654

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

The order of differentiability of the inversion operator J\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 kk guaranted by inverse function arguments, the operator J\mathcal J is everywhere differentiable andJ(k)\mathcal J^{(k)} is continuous. On the other hand, J\mathcal J is nowhere k+1k+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