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Square Roots of Elliptic Systems in Locally Uniform Domains

BuchGebunden
188 Seiten
Englisch
Springererschienen am10.09.20242024
This book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions.mehr
Verfügbare Formate
BuchGebunden
EUR139,09
E-BookPDF1 - PDF WatermarkE-Book
EUR149,79

Produkt

KlappentextThis book establishes a comprehensive theory to treat square roots of elliptic systems incorporating mixed boundary conditions under minimal geometric assumptions.

Inhalt/Kritik

Inhaltsverzeichnis
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 â 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.mehr

Schlagworte

Autor

Sebastian Bechtel is a postdoctoral researcher in the analysis group of the Delft Institute of Applied Mathematics at Delft university of Technology. He obtained his PhD in Mathematics at the Technical University of Darmstadt, Germany in 2021. His PhD studies were supported by a scholarship of "Studienstiftung des Deutschen Volkes". His research interests include harmonic analysis, PDEs, function spaces, functional calculus, and related topics.
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Bechtel, Sebastian