Overview
- Provides a self-contained introduction to the classical theory of partial differential equations (PDEs)
- Expands on the Second Edition with five new chapters, as well as new exercises and examples
- Examines how the classical approach to PDEs connects to cutting-edge research and the modeling of physical phenomena
Part of the book series: Cornerstones (COR)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
Keywords
- Partial Differential Equations
- Partial differential equations
- PDEs
- Green's Theorem
- Quasi-Linear Equations
- Laplace equation
- Boundary value problems
- Integral equations
- Heat equation
- Wave equation
- Nonlinear equations
- Linear elliptic equations
- Linear parabolic equations
- DeGiorgi classes
- Parabolic DeGiorgi classes
- Navier-Stokes equations
About this book
This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The “Problems and Complements” sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students.
Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.Reviews
“This is the third edition of a book In this third edition a good deal of new and more advanced material has been added ... . From edition to edition, this book has evolved into a rather specialized text. It is likely to be of more interest now to specialists than students new to the study of PDEs.” (Bill Satzer, MAA Reviews, February 29, 2024)
Authors and Affiliations
About the authors
Ugo Gianazza is Professor of Mathematical Analysis at the Department of Mathematics F. Casorati of the University of Pavia. His research interests include Regularity for Elliptic and Parabolic Equations. In addition to editing numerous volumes, he also co-authored the 2012 monograph Harnack's Inequality for Degenerate and Singular Parabolic Equation.
Bibliographic Information
Book Title: Partial Differential Equations
Authors: Emmanuele DiBenedetto, Ugo Gianazza
Series Title: Cornerstones
DOI: https://doi.org/10.1007/978-3-031-46618-2
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-46617-5Published: 22 October 2023
Softcover ISBN: 978-3-031-46620-5Due: 22 November 2023
eBook ISBN: 978-3-031-46618-2Published: 21 October 2023
Series ISSN: 2197-182X
Series E-ISSN: 2197-1838
Edition Number: 3
Number of Pages: XXX, 748
Number of Illustrations: 35 b/w illustrations
Topics: Analysis, Functional Analysis, Difference and Functional Equations, Integral Equations, Mathematical Modeling and Industrial Mathematics