The extension problem for fractional Sobolev spaces with a partial vanishing trace condition

Text
s00013-021-01594-0.pdf
Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.
Download (286kB)

Item Type:	Article
Type of entry:	Secondary publication
Title:	The extension problem for fractional Sobolev spaces with a partial vanishing trace condition
Language:	English
Date:	3 September 2024
Place of Publication:	Darmstadt
Year of primary publication:	2021
Place of primary publication:	Berlin
Publisher:	Springer International Publishing
Journal or Publication Title:	Archiv der Mathematik
Volume of the journal:	117
Issue Number:	1
DOI:	10.26083/tuprints-00023422
Corresponding Links:	Publisher-DOI
Origin:	Secondary publication DeepGreen
Abstract:	We construct whole-space extensions of functions in a fractional Sobolev space of order s ∈ (0, 1) and integrability p ∈ (0,∞) on an open set 0 which vanish in a suitable sense on a portion D of the boundary ∂O of 0. The set 0 is supposed to satisfy the so-called interior thickness condition in ∂O\D, which is much weaker than the global interior thickness condition. The proof works by means of a reduction to the case D = ∅ using a geometric construction.
Uncontrolled Keywords:	(Fractional) Sobolev spaces, Kondratiev spaces, Measure density condition, Extension operators, Hardy’s inequality
Status:	Publisher's Version
URN:	urn:nbn:de:tuda-tuprints-234220
Classification DDC:	500 Science and mathematics > 510 Mathematics
Divisions:	04 Department of Mathematics > Analysis
Date Deposited:	03 Sep 2024 13:35
Last Modified:	08 Oct 2024 12:14
SWORD Depositor:	Deep Green
URI:	https://tuprints.ulb.tu-darmstadt.de/id/eprint/23422
PPN:	52202453X
Export:

Actions (login required)

View Item

OAI 2.0 -Basis-URL: https://tuprints.ulb.tu-darmstadt.de/cgi /oai2 TUprints verwendet EPrints 3 .