Some inequalities on weighted Sobolev spaces, distance weights, and the Assouad dimension

Fernando López‐García and Ignacio Ojea

Mathematische Nachrichten, 2025, vol. 298, issue 8, 2749-2769

Abstract: We considercertain inequalities and a related result on weighted Sobolev spaces on bounded John domains in Rn${\mathbb {R}}^n$. Namely, we study the existence of a right inverse for the divergence operator, along with the corresponding a priori estimate, the improved and the fractional Poincaré inequalities, the Korn inequality, and the local Fefferman–Stein inequality. All these results are obtained on weighted Sobolev spaces, where the weight is a power of the distance to the boundary. In all cases the exponent of the weight d(·,∂Ω)βp$d(\cdot,\partial \Omega)^{\beta p}$ is only required to satisfy the restriction: βp>−(n−dimA(∂Ω))$\beta p>-(n-{\rm dim}_A(\partial \Omega))$, where p$p$ is the exponent of the Sobolev space and dimA(∂Ω)${\rm dim}_A(\partial \Omega)$ is the Assouad dimension of the boundary of the domain. To the best of our knowledge, this condition is less restrictive than the ones in the literature.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.70014

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:8:p:2749-2769

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().