Titlebook: Square Roots of Elliptic Systems in Locally Uniform Domains; Sebastian Bechtel Book 2024 The Editor(s) (if applicable) and The Author(s),

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Locally Uniform Domains,In this chapter, we will introduce and explore the underlying geometry for this monograph: locally uniform domains near the Neumann boundary. The precise definition will be given in Definition 2.1. The original idea of uniform domains and their relation with the Sobolev extension problem originates from Jones’ work.

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Sobolev Extension Operator,Using the results from the preceding two chapters, we craft a Sobolev extension operator in locally uniform domains near .. Our Sobolev spaces have a vanishing trace condition in . in the sense of Definition 4.1. Our precise understanding of an extension operator and the main result of this chapter are presented in Theorem 4.3.

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