Elliptic Systems of Phase Transition Type

This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes - non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-...

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Bibliographic Details
Main Author: Alikakos, Nicholas D. (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:Progress in Nonlinear Differential Equations and Their Applications, 91
Subjects:
Partial differential equations.
Calculus of variations.
Differential equations.
ISBN:9783319905723
ISSN:1421-1750 ;
Online Access: Get full text
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Table of Contents:
  • Introduction
  • Connections
  • Basics for the PDE System
  • The Cut-Off Lemma and a Maximum Principle
  • Estimates
  • Symmetry and the Vector Allen-Cahn Equation: the Point Group in Rn
  • Symmetry and the Vector Allen-Cahn Equation: Crystalline and Other Complex Structures
  • Hierarchical Structure - Stratification
  • Vector Minimizers in R2
  • Radial Solutions of ∆u = c2u.

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