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Estimates on translations and Taylor expansions in fractional Sobolev spaces

Abstract:

In this paper we study how the (normalised) Gagliardo semi-norms [u]Ws,p(Rn) control translations. In particular, we prove that ||u(·+y)−u ||Lp(Rn) ≤ C[u]Ws,p(Rn) |y| s for n ≥ 1, s ∈ [0, 1] and p ∈ [1, +∞], where C depends only on n. We then obtain a corresponding higher-order version of this result: we get fractional rates of the error term in the Taylor expansion. We also present relevant implications of our two results. First, we obtain a direct...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.na.2020.111995

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Sub department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier Publisher's website
Journal:
Nonlinear Analysis Journal website
Volume:
200
Article number:
111995
Publication date:
2020-05-29
Acceptance date:
2020-05-20
DOI:
ISSN:
0362-546X
Language:
English
Keywords:
Pubs id:
1137521
Local pid:
pubs:1137521
Deposit date:
2020-10-14

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