Square Roots of Elliptic Systems in Locally Uniform Domains
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Beschreibung
This book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions. To lay the groundwork, the text begins by introducing the geometry of locally uniform domains and establishes theory for function spaces on locally uniform domains, including interpolation theory and extension operators. In these introductory parts, fundamental knowledge on function spaces, interpolation theory and geometric measure theory and fractional dimensions are recalled, making the main content of the book easier to comprehend. The centerpiece of the book is the solution to Kato's square root problem on locally uniform domains. The Kato result is complemented by corresponding Lᵖ bounds in natural intervals of integrability parameters.
This book will be useful to researchers in harmonic analysis, functional analysis and related areas.
This book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions. To lay the groundwork, the text begins by introducing the geometry of locally uniform domains and establishes theory for function spaces on locally uniform domains, including interpolation theory and extension operators. In these introductory parts, fundamental knowledge on function spaces, interpolation theory and geometric measure theory and fractional dimensions are recalled, making the main content of the book easier to comprehend. The centerpiece of the book is the solution to Kato's square root problem on locally uniform domains. The Kato result is complemented by corresponding Lᵖ bounds in natural intervals of integrability parameters.
This book will be useful to researchers in harmonic analysis, functional analysis and related areas.
Provides a complete framework to treat elliptic and parabolic problems incorporating mixed boundary conditions Introduces global approaches to cover problems subject to mixed boundary conditions Solves Kato's square root problem under minimal geometric requirements
Autor*in
Sebastian Bechtel
Themen in »Square Roots of Elliptic Systems in Locally Uniform Domains«
Mixed Boundary Conditions Function Spaces Extension Operators Hardy's Inequality Kato's Square Root Problem Riesz Transforms Fractional Laplacian Functional Calculus Sobolev Spaces Interpolation Theory
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“Addressing non-smoothness has been a significant focus in the analysis of partial differential equations and other branches of analysis over the past few decades. This book, which evolved from the author's PhD thesis, presents their contributions to the field in a streamlined manner. … This book delves deeply into these themes and provides state-of-the-art results for square roots of elliptic systems in locally uniform domains.” (Lubomira G. Softova, Mathematical Reviews, June, 2025)
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