Overview
- Outgrowth of Moser–Bangert's work on solutions of a family of nonlinear elliptic partial differential equations
- Develops and examines the rich structure of the set of solutions of the simpler model case (PDE)
- Minimization arguments are an important tool in the investigation
- Unique book in the literature
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 81)
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Table of contents (13 chapters)
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Front Matter
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Basic Solutions
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Front Matter
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Solutions of (PDE) Defined on $$\mathbb{R}^2 \times \mathbb{T}^{n-2}$$
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Front Matter
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Solutions of (PDE) Defined on R2 × Tn-2
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Back Matter
Keywords
About this book
This monograph presents extensions of the Moser–Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen–Cahn PDE model of phase transitions.
After recalling the relevant Moser–Bangert results, Extensions of Moser–Bangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained.
The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.
Reviews
From the reviews:
“This book contains a study of the solution set to (PDE), expanding work by Moser and Bangert and previous work by the authors for (AC). … This is an important piece of work concerning a difficult and deep matter. … This a very good demonstration of the power of variational methods, showing that they can be modified, extended and combined in order to deal with many different kinds of problems.” (Jesús Hernández, Mathematical Reviews, Issue 2012 m)
Authors and Affiliations
Bibliographic Information
Book Title: Extensions of Moser–Bangert Theory
Book Subtitle: Locally Minimal Solutions
Authors: Paul H. Rabinowitz, Edward W. Stredulinsky
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-0-8176-8117-3
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-0-8176-8116-6Published: 24 June 2011
eBook ISBN: 978-0-8176-8117-3Published: 16 June 2011
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: VIII, 208
Topics: Partial Differential Equations, Calculus of Variations and Optimal Control; Optimization, Dynamical Systems and Ergodic Theory, Analysis, Food Science