Unique Continuation Properties for Partial Differential Equations: Introduction to the Stability Estimates for Inverse Problems
暫譯: 偏微分方程的獨特延續性質：逆問題穩定性估計的介紹

Vessella, Sergio

Unique Continuation Properties for Partial Differential Equations: Introduction to the Stability Estimates for Inverse Problems
  • 出版商: Springer
  • 出版日期: 2025-04-30
  • 售價: $4,650
  • 貴賓價: 9.8 折 $4,557
  • 語言: 英文
  • 頁數: 957
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031863658
  • ISBN-13: 9783031863653
  • 相關分類: 微積分 Calculus

    • 海外代購書籍(需單獨結帳)

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商品描述

This book provides a comprehensive and self-contained introduction to the study of the Cauchy problem and unique continuation properties for partial differential equations. Aimed at graduate and advanced undergraduate students, it bridges foundational concepts such as Lebesgue measure theory, functional analysis, and partial differential equations with advanced topics like stability estimates in inverse problems and quantitative unique continuation. By presenting detailed proofs and illustrative examples, the text equips readers with a deeper understanding of these fundamental topics and their applications in mathematical analysis. Designed to serve as both a learning resource and a reference, this book is particularly suited for those pursuing research in mathematical physics, inverse problems, or applied analysis.

商品描述(中文翻譯)

本書提供了對於Cauchy問題及偏微分方程的唯一延續性特性的全面且自成一體的介紹。針對研究生及高年級本科生，本書將基礎概念如Lebesgue測度理論、泛函分析及偏微分方程與進階主題如逆問題中的穩定性估計及定量唯一延續性相結合。透過詳細的證明和示例，本書使讀者對這些基本主題及其在數學分析中的應用有更深入的理解。本書旨在作為學習資源和參考資料，特別適合那些從事數學物理、逆問題或應用分析研究的人士。

作者簡介

Sergio Vessella was born on August 20 1955. He graduated from Pisa University in 1978. He held a CNR grant (1979--1982) and served as a CNR Researcher (1982--1988). He became Associate Professor in 1988 and in 2001 he was promoted Full Professor. His research focuses on Inverse Problems (IP) for Partial Differetial Equations (PDEs) and Quantitative Estimates of Unique Continuation for PDEs. He co-authored Abel Integral Equations with Prof. R. Gorenflo (Springer LNM, 1991). His work spans IP for Elliptic, Parabolic, and Hyperbolic equation, size estimates in inclusion problems, Lipschitz dependence of coefficients, and Strong Unique Continuation Properties for PDEs. Prof. Vessella has collaborated with leading mathematicians, including Profs. G. Alessandrini, M. De Hoop, and L. Escauriaza. He has served as visiting professor in Berlin, Linz, Rutgers, and others insitutions. He has organized symposia (e.g., IFIP-2005, Turin) and courses (e.g., Firenze, 2006) and has been an invited speaker at international conferences (e.g., Oberwolfach, Potsdam, IPMS-Malta 2024).

作者簡介(中文翻譯)

Sergio Vessella 於1955年8月20日出生。他於1978年畢業於比薩大學。他曾獲得CNR獎學金（1979--1982），並擔任CNR研究員（1982--1988）。他於1988年成為副教授，並於2001年晉升為正教授。他的研究專注於偏微分方程（PDEs）的反問題（Inverse Problems, IP）以及PDEs的唯一延續的定量估計。他與R. Gorenflo教授共同撰寫了《Abel Integral Equations》（Springer LNM, 1991）。他的研究涵蓋了橢圓、拋物和雙曲方程的反問題、包含問題中的大小估計、係數的Lipschitz依賴性，以及PDEs的強唯一延續性質。Vessella教授與多位領先的數學家合作，包括G. Alessandrini、M. De Hoop和L. Escauriaza教授。他曾在柏林、林茲、羅格斯大學等機構擔任訪問教授。他組織過研討會（例如，IFIP-2005，都靈）和課程（例如，佛羅倫斯，2006），並在國際會議上擔任邀請演講者（例如，Oberwolfach、波茨坦、IPMS-馬爾他2024）。

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