A note on properties of the restriction operator on Sobolev spaces

Hewett, D. P. and Moiola, A. (2017) A note on properties of the restriction operator on Sobolev spaces. Journal of Applied Analysis, 23 (1). pp. 1-8. ISSN 1425-6908 doi: 10.1515/jaa-2017-0001

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71844
Identification Number/DOI	10.1515/jaa-2017-0001
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	De Gruyter
Download/View statistics	View download statistics for this item