1. A second order approach to the Kato square root problem on open sets
- Author
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Bechtel, Sebastian, Hutcheson, Cody, Schmatzler, Tim, Tasci, Tolgahan, and Wittig, Mattes
- Subjects
Mathematics - Functional Analysis ,Mathematics - Analysis of PDEs ,Mathematics - Classical Analysis and ODEs - Abstract
We give a proof for the Kato square root problem on suitable open sets and subject to pure Dirichlet boundary conditions. In contrast to earlier work, our proof uses only second-order techniques and is in the spirit of the proof given by Egert--Haller--Monniaux--Tolksdorf in the scope of the 27th international internet seminar for $\Omega = \mathbb{R}^n$. In contrast to the usual proofs based on the first-order framework by Axelsson--Keith--McIntosh, the proof becomes substantially shorter and technically less demanding., Comment: 25 pages. Article written in the scope of ISEM27
- Published
- 2024