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

Gyula Farkas | Zendy; Barnabás M. Garay | Zendy

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

Author(s) -

Gyula Farkas,

Barnabás M. Garay

Publication year - 2000

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/972

Subject(s) - sobolev space , differentiable function , inversion (geology) , mathematics , operator (biology) , mathematical analysis , pure mathematics , geology , geomorphology , structural basin , chemistry , biochemistry , repressor , transcription factor , gene

The order of differentiability of the inversion operator 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 J is everywhere differentiable and J (k) is continuous. On the other hand, J is nowhere k +1 times differentiable.

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