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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Elliptic Systems of Phase Transition Type

Elliptic Systems of Phase Transition Type

Alikakos, Nicholas D.
Fusco, Giorgio
Smyrnelis, Panayotis

Hardcover

Series: Progress in Nonlinear Differential Equations and Their Appli, Book 91

CalculusGeneral Mathematics

ISBN10: 3319905716
ISBN13: 9783319905716
Publisher: Birkhauser
Published: Jan 31 2019
Pages: 343
Weight: 1.48
Height: 0.81 Width: 6.14 Depth: 9.21
Language: English

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.

Key features and topics of this self-contained, systematic exposition include:

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