Coverart for item
The Resource Elliptic Systems of Phase Transition Type, by Nicholas D. Alikakos, Giorgio Fusco, Panayotis Smyrnelis, (electronic resource)

Elliptic Systems of Phase Transition Type, by Nicholas D. Alikakos, Giorgio Fusco, Panayotis Smyrnelis, (electronic resource)

Label
Elliptic Systems of Phase Transition Type
Title
Elliptic Systems of Phase Transition Type
Statement of responsibility
by Nicholas D. Alikakos, Giorgio Fusco, Panayotis Smyrnelis
Creator
Contributor
Author
Subject
Language
eng
Summary
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: • Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions. • Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves. • Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates. • Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results. This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Alikakos, Nicholas D
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Fusco, Giorgio
  • Smyrnelis, Panayotis
Series statement
  • Progress in Nonlinear Differential Equations and Their Applications,
  • Springer eBooks
  • Springer eBooks.
Series volume
91
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Mathematical optimization
  • Differential Equations
Label
Elliptic Systems of Phase Transition Type, by Nicholas D. Alikakos, Giorgio Fusco, Panayotis Smyrnelis, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-90572-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
978-3-319-90572-3
Dimensions
unknown
Extent
1 online resource (XII, 343 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319905723
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
59 illustrations, 10 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1083760490
Label
Elliptic Systems of Phase Transition Type, by Nicholas D. Alikakos, Giorgio Fusco, Panayotis Smyrnelis, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-319-90572-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
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
Control code
978-3-319-90572-3
Dimensions
unknown
Extent
1 online resource (XII, 343 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319905723
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
59 illustrations, 10 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1083760490

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