Square Roots of Elliptic Systems in Locally Uniform Domains
Bechtel, Sebastian
- 出版商: Birkhauser Boston
- 出版日期: 2024-10-18
- 售價: $6,190
- 貴賓價: 9.5 折 $5,881
- 語言: 英文
- 頁數: 162
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3031637674
- ISBN-13: 9783031637674
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商品描述
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 $L^p$ bounds in natural intervals of integrability parameters.
This book will be useful to researchers in harmonic analysis, functional analysis and related areas.
商品描述(中文翻譯)
本書建立了一個全面的理論,以最小的幾何假設來處理包含混合邊界條件的橢圓系統的平方根。為了奠定基礎,本文首先介紹了局部均勻域的幾何形狀,並建立了關於局部均勻域上的函數空間的理論,包括插值理論和擴展算子。在這些介紹部分中,回顧了關於函數空間、插值理論、幾何測度理論和分數維度的基本知識,使得本書的主要內容更容易理解。本書的核心是解決了在局部均勻域上的Kato平方根問題。Kato的結果通過相應的$L^p$界限在自然可積參數的區間中得到補充。本書將對調和分析、泛函分析和相關領域的研究人員有所幫助。
作者簡介
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.
作者簡介(中文翻譯)
Sebastian Bechtel是荷蘭科技大學Delft應用數學研究所分析組的博士後研究員。他於2021年在德國達姆施塔特工業大學獲得數學博士學位,並獲得德國人民研究基金會的獎學金支持。他的研究興趣包括調和分析、偏微分方程、函數空間、函數計算等相關主題。