Regularity Techniques for Elliptic Pdes and the Fractional Laplacian
暫譯: 橢圓偏微分方程的正則性技術與分數拉普拉斯算子

Stinga, Pablo Raúl

Regularity Techniques for Elliptic Pdes and the Fractional Laplacian
  • 出版商: CRC
  • 出版日期: 2024-06-21
  • 售價: $5,800
  • 貴賓價: 9.5 折 $5,510
  • 語言: 英文
  • 頁數: 318
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1032679441
  • ISBN-13: 9781032679440
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian. The emphasis is placed on ideas and the development of intuition, while at the same time being completely rigorous. The reader should keep in mind that this text is about how analysis can be applied to regularity estimates. Many methods are nonlinear in nature, but the focus is on linear equations without lower order terms, thus avoiding bulky computations. The philosophy underpinning the book is that ideas must be flushed out in the cleanest and simplest ways, showing all the details and always maintaining rigor.

Features

  • Self-contained treatment of the topic
  • Bridges the gap between upper undergraduate textbooks and advanced monographs to offer a useful, accessible reference for students and researchers.
  • Replete with useful references.

商品描述(中文翻譯)

《橢圓偏微分方程的正則性技術與分數拉普拉斯算子》介紹了重要的分析和幾何技術，以證明第二階橢圓方程（無論是散度形式還是非散度形式）及由分數拉普拉斯算子驅動的非局部方程的解的正則性估計。重點放在概念和直覺的發展上，同時保持完全的嚴謹性。讀者應該記住，這本書是關於如何將分析應用於正則性估計。許多方法本質上是非線性的，但重點放在沒有低階項的線性方程上，從而避免繁瑣的計算。本書的哲學是，概念必須以最乾淨和最簡單的方式表達，顯示所有細節並始終保持嚴謹性。

特點：
- 獨立完整的主題處理
- 橋接本科生教材與高級專著之間的差距，為學生和研究人員提供有用且易於接觸的參考資料
- 充滿有用的參考文獻

作者簡介

Pablo Raúl Stinga earned his Licenciatura en Ciencias Matemáticas degree at Universidad Nacional de San Luis, in San Luis, Argentina (2005). He earned his Máster en Matemáticas y Aplicaciones (2007), and his Doctorado en Matemáticas Doctor Europeus under the direction of José L.Torrea at Universidad Autόnoma de Madrid, Spain (2010). He held postdoctoral research positions at Universidad de Zaragoza, Spain (2010) and Universidad de La Rioja, Spain (2011-2012). During the period 2012-2015, he was the R.H. Bing Fellow in Mathematics No.1 Instructor at the University of Texas at Austin, USA, where he worked as a postdoctoral researcher under the supervision of Luis A. Caffarelli. He is currently Associate Professor at Iowa State University, USA. His research interests are in analysis, partial differential equations and nonlocal fractional equations.

作者簡介(中文翻譯)

Pablo Raúl Stinga 於阿根廷聖路易斯國立大學獲得數學科學學士學位（Licenciatura en Ciencias Matemáticas，2005年）。他於2007年獲得數學與應用碩士學位（Máster en Matemáticas y Aplicaciones），並在西班牙馬德里自治大學（Universidad Autónoma de Madrid）在José L. Torrea的指導下獲得歐洲博士學位（Doctorado en Matemáticas Doctor Europeus，2010年）。他曾在西班牙薩拉戈薩大學（Universidad de Zaragoza，2010年）和拉里奧哈大學（Universidad de La Rioja，2011-2012年）擔任博士後研究職位。在2012年至2015年間，他是美國德克薩斯州奧斯汀大學的R.H. Bing數學研究員No.1講師，並在Luis A. Caffarelli的指導下擔任博士後研究員。目前，他是美國愛荷華州立大學的副教授。他的研究興趣包括分析學、偏微分方程和非局部分數方程。

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