Pointwise inequalities for Sobolev functions on generalized cuspidal domains
Abstract
Olkoon Ω⊂Rn−1 rajoitettu tähtimäinen alue ja Ωψ ulkoneva kärkialue, jonka kanta-alue on Ω. Arvoilla 1< p≤ ∞ osoitamme, että W1,p(Ωψ) = M1,p(Ωψ) jos ja vain jos W1,p(Ω) = M1,p(Ω).
Let Ω⊂Rn−1 be a bounded star-shaped domain and Ωψ be an outward cuspidal domain with base domain Ω. We prove that for 1< p≤ ∞, W1,p(Ωψ) = M1,p(Ωψ) if and only if W1,p(Ω) = M1,p(Ω).
Let Ω⊂Rn−1 be a bounded star-shaped domain and Ωψ be an outward cuspidal domain with base domain Ω. We prove that for 1< p≤ ∞, W1,p(Ωψ) = M1,p(Ωψ) if and only if W1,p(Ω) = M1,p(Ω).
Main Author
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Finnish Mathematical Society
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202208194258Use this for linking
Review status
Peer reviewed
ISSN
2737-0690
DOI
https://doi.org/10.54330/afm.117881
Language
English
Published in
Annales Fennici mathematici
Citation
- Zhu, Z. (2022). Pointwise inequalities for Sobolev functions on generalized cuspidal domains. Annales Fennici mathematici, 47(2), 747-757. https://doi.org/10.54330/afm.117881
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
The author has been supported by the Academy of Finland via Centre of Excellence in Analysisand Dynamics Research (Project #323960).
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