03790nam a22005655i 4500 978-3-031-63768-1 DE-He213 20251030112946.0 cr nn 008mamaa 240910s2024 sz | s |||| 0|eng d 9783031637681 978-3-031-63768-1 10.1007/978-3-031-63768-1 doi QA370-380 PBKJ bicssc MAT007000 bisacsh PBKJ thema Bechtel, Sebastian. author. aut http://id.loc.gov/vocabulary/relators/aut 83963 Square Roots of Elliptic Systems in Locally Uniform Domains [electronic resource] / by Sebastian Bechtel. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Birkhäuser, 2024. IX, 188 p. 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Linear Operators and Linear Systems, 2504-3617 ; 303 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. 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. Differential equations. Functional analysis. Operator theory. Functions of real variables. 83964 Differential Equations. Functional Analysis. Operator Theory. Real Functions. 83965 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031637674 Printed edition: 9783031637698 Printed edition: 9783031637704 Linear Operators and Linear Systems, 2504-3617 ; 303 83966 https://doi.org/10.1007/978-3-031-63768-1 ZDB-2-SMA ZDB-2-SXMS 63219 63219