Unique Continuation Properties for Partial Differential Equations
Introduction to the Stability Estimates for Inverse Problems
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Explains unique continuation for PDE, combining basic and advanced topics for graduate and advanced students Introduces the quantitative use of Carleman estimates, crucial for inverse problems and applied mathematics Integrates boundary problems and unique continuation in a clear, self-contained framework
Autor*in
Sergio Vessella
Themen in »Unique Continuation Properties for Partial Differential Equations«
Partial Differential Equations Unique Continuation Properties Quantitative Estimates of Unique Continuation Ill-Posed Problems Stability Estimates Inverse Problems
Stimmen zu »Unique Continuation Properties for Partial Differential Equations«
“The book provides an accessible ‘bridge’ between rigorous PDE analysis and the more specialized topics on UCPs and stability estimates in inverse problems. It complements the standard PDE textbooks ... . It can be used not only as a textbook for graduate and advanced undergraduate students, but also as a reference for researchers entering areas such as inverse problems, control theory, or any mathematical branch where the UCPs play an important role.” (Shitao Liu, Mathematical Reviews, April, 2026)
()