Weighted Hardy inequalities beyond Lipschitz domains
Abstract
It is a well-known fact that in a Lipschitz domain Ω ⊂ R
n
a p-Hardy inequality, with weight dist(x, ∂Ω)β
, holds for all u ∈ C
∞0 (Ω)
whenever β < p − 1. We show that actually the same is true under
the sole assumption that the boundary of the domain satisfies a uniform
density condition with the exponent λ = n − 1. Corresponding results
also hold for smaller exponents, and, in fact, our methods work in general
metric spaces satisfying standard structural assumptions.
Main Author
Format
Articles
Research article
Published
2014
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201512144007Use this for linking
Review status
Peer reviewed
ISSN
0002-9939
DOI
https://doi.org/10.1090/S0002-9939-2014-11904-6
Language
English
Published in
Proceedings of the American Mathematical Society
Citation
- Lehrbäck, J. (2014). Weighted Hardy inequalities beyond Lipschitz domains. Proceedings of the American Mathematical Society, 142(5), 1705-1715. https://doi.org/10.1090/S0002-9939-2014-11904-6
License
Copyright© 2014 American Mathematical Society. This is a final draft version of an article whose final and definitive form has been published by AMS. Published in this repository with the kind permission of the publisher.