Magnetic fractional Poincaré inequality in punctured domains
Abstract
We study Poincaré-Wirtinger type inequalities in the framework of magnetic fractional Sobolev spaces. In the local case, Lieb et al. (2003) [19] showed that, if a bounded domain Ω is the union of two disjoint sets Γ and Λ, then the Lp-norm of a function calculated on Ω is dominated by the sum of magnetic seminorms of the function, calculated on Γ and Λ separately. We show that the straightforward generalisation of their result to nonlocal setup does not hold true in general. We provide an alternative formulation of the problem for the nonlocal case. As an auxiliary result, we also show that the set of eigenvalues of the magnetic fractional Laplacian is discrete.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202401251548Use this for linking
Review status
Peer reviewed
ISSN
0022-247X
DOI
https://doi.org/10.1016/j.jmaa.2024.128103
Language
English
Published in
Journal of Mathematical Analysis and Applications
Citation
- Bal, K., Mohanta, K., & Roy, P. (2024). Magnetic fractional Poincaré inequality in punctured domains. Journal of Mathematical Analysis and Applications, 535(1), Article 128103. https://doi.org/10.1016/j.jmaa.2024.128103
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Funder(s)
Research Council of Finland
Funding program(s)
Akatemiahanke, SA
Academy Project, AoF
Additional information about funding
Research work of the first author is funded by Matrics grant (MTR/2020/000594). Research work of the second author is funded by Academy of Finland (Suomen Akatemia) grant: Geometrinen Analyysi (21000046081). Research work of the third author is funded by Matrics grant (MTR/2019/000585) and by Core Research Grant (CRG/2022/007867) of SERB.
Copyright© 2024 The Author(s). Published by Elsevier Inc.