Elliptic Systems of Phase Transition Type (Progress in Nonlinear Differential Equations and Their Applications #91)

By: and and

Sign Up Now! Already a Member? Log In
You must be logged into Bookshare to access this title. Learn about membership options, or view our freely available titles.

Synopsis
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-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin's proof. It also introduces an alternative method for obtaining pointwise estimates.
Copyright:
2018

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9783319905723
Publisher:
Springer International Publishing
Date of Addition:
Copyrighted By:
Springer Nature Switzerland AG
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Mathematics and Statistics
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

Reviews

No Rating Yet