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Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces
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Fefferman, C. L., Hajduk, K. W. and Robinson, James C. (2022) Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces. Proceedings of the London Mathematical Society, 125 (4). pp. 759-777. doi:10.1112/plms.12469 ISSN 0024-6115 .
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Official URL: https://doi.org/10.1112/plms.12469
Abstract
We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue spaces. We prove an abstract result referred to fractional power spaces of positive, self-adjoint, compact-inverse operators on Hilbert spaces, and then obtain our main result by using the explicit form of these fractional power spaces for the Dirichlet Laplacian and Stokes operators. As a simple application, we prove that all weak solutions of the convective Brinkman–Forchheimer equations posed on a bounded domain in
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Partial, Eigenfunctions, Linear operators | ||||||||||||
| Journal or Publication Title: | Proceedings of the London Mathematical Society | ||||||||||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | ||||||||||||
| ISSN: | 0024-6115 | ||||||||||||
| Official Date: | October 2022 | ||||||||||||
| Dates: |
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| Volume: | 125 | ||||||||||||
| Number: | 4 | ||||||||||||
| Page Range: | pp. 759-777 | ||||||||||||
| DOI: | 10.1112/plms.12469 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Date of first compliant deposit: | 9 June 2022 | ||||||||||||
| Date of first compliant Open Access: | 21 July 2022 | ||||||||||||
| RIOXX Funder/Project Grant: |
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