Hewett, DP;
Moiola, A;
(2017)
A note on properties of the restriction operator on Sobolev spaces.
Journal of Applied Analysis
, 23
(1)
pp. 1-8.
10.1515/jaa-2017-0001.
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Abstract
In our companion paper [3] we studied a number of different Sobolev spaces on a general (non-Lipschitz) open subset Ω of Rn, defined as closed subspaces of the classical Bessel potential spaces Hs(Rn) for s∈R. These spaces are mapped by the restriction operator to certain spaces of distributions on Ω. In this note we make some observations about the relation between these spaces of global and local distributions. In particular, we study conditions under which the restriction operator is or is not injective, surjective and isometric between given pairs of spaces. We also provide an explicit formula for minimal norm extension (an inverse of the restriction operator in appropriate spaces) in a special case.
| Type: | Article |
|---|---|
| Title: | A note on properties of the restriction operator on Sobolev spaces |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/jaa-2017-0001 |
| Publisher version: | https://doi.org/10.1515/jaa-2017-0001 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Bessel potential Sobolev spaces; non-Lipschitz domains; restriction operator; s-nullity,unitary realisations of dual spaces; minimal norm extension |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1563652 |
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