Remarks on Sobolev norms of fractional orders

Remarks on Sobolev norms of fractional orders

When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm as a function on the smaller set compared to its norm on the whole domain? On what do the comparison constants depend o...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 498; no. 2; p. 124960
Main Author: Tran, Thanh
Format: Journal Article
Language:English
Published: Elsevier Inc 15-06-2021
Subjects:
Fractional-order Sobolev spaces
Interpolation norms
Sobolev-Slobodetski norms
Fractional-order Sobolev spaces
Interpolation norms
Sobolev-Slobodetski norms
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Summary:When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm as a function on the smaller set compared to its norm on the whole domain? On what do the comparison constants depend on? Do different norms behave differently? This article addresses these issues. We prove some inequalities and disprove some misconceptions by counter-examples.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.124960