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Singularities in PDE and the Calculus of Variations

Edited by: Stanley Alama McMaster University, Hamilton, ON, Canada
Lia Bronsard McMaster University, Hamilton, ON, Canada
Peter J. Sternberg Indiana University, Bloomington, IN
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Softcover ISBN: 978-0-8218-4350-5
Product Code: CRMP/44
List Price: $112.00 MAA Member Price:$100.80
AMS Member Price: $89.60 Electronic ISBN: 978-1-4704-3958-3 Product Code: CRMP/44.E List Price:$105.00
MAA Member Price: $94.50 AMS Member Price:$84.00
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List Price: $168.00 MAA Member Price:$151.20
AMS Member Price: $134.40 Click above image for expanded view Singularities in PDE and the Calculus of Variations Edited by: Stanley Alama McMaster University, Hamilton, ON, Canada Lia Bronsard McMaster University, Hamilton, ON, Canada Peter J. Sternberg Indiana University, Bloomington, IN A co-publication of the AMS and Centre de Recherches Mathématiques Available Formats:  Softcover ISBN: 978-0-8218-4350-5 Product Code: CRMP/44  List Price:$112.00 MAA Member Price: $100.80 AMS Member Price:$89.60
 Electronic ISBN: 978-1-4704-3958-3 Product Code: CRMP/44.E
 List Price: $105.00 MAA Member Price:$94.50 AMS Member Price: $84.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$168.00 MAA Member Price: $151.20 AMS Member Price:$134.40
• Book Details

CRM Proceedings & Lecture Notes
Volume: 442008; 267 pp
MSC: Primary 35; 47;

This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampère functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.

Graduate students and research mathematicians interested in PDEs and calculus of variation.

• Chapters
• Variational problems arising in biology
• On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation
• Nonlocal Cahn-Hilliard and isoperimetric problems: Periodic phase separation induced by competing long- and short-range interactions
• On a generalized Ginzburg-Landau energy for superconducting/normal composite materials
• Global questions for map evolution equations
• Pohožaev-type identities for an elliptic equation
• Some remarks on Monge-Ampère functions
• Variational versus pde-based approaches in mathematical image processing
• On the energy of a Chern-Simons-Higgs vortex lattice
• Some recent results about a class of singularly perturbed elliptic equations
• The dipole problem for $H^{1/2}(\mathbb {S}^2;\mathbb {S}^1)$-maps and application
• Hodge decompositions, $\Gamma$-convergence and the Gross-Pitaevskii energy
• Bifurcation of vortex solutions to a Ginzburg-Landau equation in an annulus
• An Allen-Cahn type problem with curvature modification
• Rare events, action minimization, and sharp interface limits
• The Gauss-Green theorem for weakly differentiable vector fields

• Request Review Copy
Volume: 442008; 267 pp
MSC: Primary 35; 47;

This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampère functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.

Graduate students and research mathematicians interested in PDEs and calculus of variation.

• Chapters
• Variational problems arising in biology
• On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation
• Nonlocal Cahn-Hilliard and isoperimetric problems: Periodic phase separation induced by competing long- and short-range interactions
• On a generalized Ginzburg-Landau energy for superconducting/normal composite materials
• Global questions for map evolution equations
• Pohožaev-type identities for an elliptic equation
• Some remarks on Monge-Ampère functions
• Variational versus pde-based approaches in mathematical image processing
• On the energy of a Chern-Simons-Higgs vortex lattice
• Some recent results about a class of singularly perturbed elliptic equations
• The dipole problem for $H^{1/2}(\mathbb {S}^2;\mathbb {S}^1)$-maps and application
• Hodge decompositions, $\Gamma$-convergence and the Gross-Pitaevskii energy
• Bifurcation of vortex solutions to a Ginzburg-Landau equation in an annulus
• An Allen-Cahn type problem with curvature modification
• Rare events, action minimization, and sharp interface limits
• The Gauss-Green theorem for weakly differentiable vector fields
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