Square Roots of Elliptic Systems in Locally Uniform Domains / by Sebastian Bechtel.

Format:

Book

Author/Creator:

Bechtel, Sebastian.

Series:

Linear Operators and Linear Systems, 2504-3617 ; 303

Language:

English

Subjects (All):

Differential equations.

Functional analysis.

Operator theory.

Functions of real variables.

Differential Equations.

Functional Analysis.

Operator Theory.

Real Functions.

Local Subjects:

Differential Equations.

Functional Analysis.

Operator Theory.

Real Functions.

Physical Description:

1 online resource (191 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2024.

Summary:

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.

Contents:

Introduction

Locally uniform domains

A density result for locally uniform domains

Sobolev extension operator

A short account on sectorial and bisectorial operators

Elliptic systems in divergence form

Porous sets

Sobolev spaces with a vanishing trace condition

Hardy’s inequality

Real interpolation of Sobolev spaces

Higher regularity for fractional powers of the Laplacian

First order formalism

Kato’s square root property on thick sets

Removing the thickness condition

Interlude: Extension operators for fractional Sobolev spaces

Critical numbers and Lp − Lq bounded families of operators

Lp-bounds for the H1-calculus and Riesz transform

Calder´on–Zygmund decomposition for Sobolev functions

Lp bounds for square roots of elliptic systems

References

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-63768-2

OCLC:

1455760019