Extensions of Moser–Bangert Theory Locally Minimal Solutions /

• Main Authors: Rabinowitz, Paul H. (Author), Stredulinsky, Edward W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2011.
• Series: Progress in Nonlinear Differential Equations and Their Applications ; 81
• Subjects: Mathematics.; Food > Biotechnology.; Mathematical analysis.; Analysis (Mathematics).; Dynamics.; Ergodic theory.; Partial differential equations.; Calculus of variations.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.; Dynamical Systems and Ergodic Theory.; Analysis.; Food Science.

With the goal of establishing a version for partial differential equations (PDEs) of the Aubry–Mather theory of monotone twist maps, Moser and then Bangert studied solutions of their model equations that possessed certain minimality and monotonicity properties. This monograph presents extensions of...

Table of Contents:

• 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.