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A second-order approach to the Kato square root problem on open sets
Citation Link: https://doi.org/10.15480/882.16952
Publikationstyp
Journal Article
Date Issued
2026-06-01
Sprache
English
Author(s)
Hutcheson, Cody
Schmatzler, Timotheus
Tasci, Tolgahan
Wittig, Mattes
TORE-DOI
Journal
Volume
26
Issue
2
Article Number
45
Citation
Journal of Evolution Equations 26 (2): 45 (2026)
Publisher DOI
Scopus ID
Publisher
Springer
We obtain the Kato square root property for coupled second-order elliptic systems in divergence form subject to mixed boundary conditions on an open and possibly unbounded set in Rn under two simple geometric conditions: The Dirichlet boundary parts for the respective components are Ahlfors–David regular and a quantitative connectivity property in the spirit of locally uniform domains holds near the remaining Neumann boundary parts. In contrast with earlier work, our proof is not based on the first-order approach due to Axelsson–Keith–McIntosh but uses a second-order approach in the spirit of the original solution to the Kato square root problem on Euclidean space. This way, the proof becomes substantially shorter and technically less demanding.
Subjects
Ahlfors–David regular sets
Kato square root problem
Locally uniform domains
Second-order approach
T(b)-argument
DDC Class
515.3: Differential calculus and equations
Publication version
publishedVersion
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