Rabinowitz / Stredulinsky Extensions of Moser–Bangert Theory

Locally Minimal Solutions
1. Auflage 2011
ISBN: 978-0-8176-8117-3
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 81, 208 Seiten, eBook

Reihe: Progress in Nonlinear Differential Equations and Their Applications

This monograph presents extensions of the Moser–Bangert approach that include solutions of a family of nonlinear elliptic PDEs on  R n  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.

Zielgruppe

Research

Autoren/Hrsg.

Rabinowitz, Paul H.

Stredulinsky, Edward W.

Inhaltsverzeichnis

1 Introduction.- Part I: Basic Solutions.- 2 Function Spaces and the First Renormalized Functional.- 3 The Simplest Heteroclinics.- 4 Heteroclinics in x1 and x2.- 5 More Basic Solutions.- Part II: Shadowing Results.- 6 The Simplest Cases.- 7 The Proof of Theorem 6.8.- 8 k-Transition Solutions for k > 2.- 9 Monotone 2-Transition Solutions.- 10 Monotone Multitransition Solutions.- 11 A Mixed Case.- Part III: Solutions of (PDE) Defined on R^2 x T^{n-2}.- 12 A Class of Strictly 1-Monotone Infinite Transition Solutions of (PDE).- 13 Solutions of (PDE) with Two Transitions in x1 and Heteroclinic Behavior in x2