Softcover ISBN:  9780821843505 
Product Code:  CRMP/44 
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Electronic ISBN:  9781470439583 
Product Code:  CRMP/44.E 
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Book DetailsCRM Proceedings & Lecture NotesVolume: 44; 2008; 267 ppMSC: 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 CahnHilliard model of phase transitions and domain walls; vortices in GinzburgLandau type models for superconductivity and superfluidity; the OhnaKawasaki model for diblock copolymers; models of image enhancement; and MongeAmpère 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.
ReadershipGraduate students and research mathematicians interested in PDEs and calculus of variation.

Table of Contents

Chapters

Variational problems arising in biology

On the Cauchy problem for phase and vortices in the parabolic GinzburgLandau equation

Nonlocal CahnHilliard and isoperimetric problems: Periodic phase separation induced by competing long and shortrange interactions

On a generalized GinzburgLandau energy for superconducting/normal composite materials

Global questions for map evolution equations

Pohožaevtype identities for an elliptic equation

Some remarks on MongeAmpère functions

Variational versus pdebased approaches in mathematical image processing

On the energy of a ChernSimonsHiggs 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 GrossPitaevskii energy

Bifurcation of vortex solutions to a GinzburgLandau equation in an annulus

An AllenCahn type problem with curvature modification

Rare events, action minimization, and sharp interface limits

The GaussGreen theorem for weakly differentiable vector fields


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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 CahnHilliard model of phase transitions and domain walls; vortices in GinzburgLandau type models for superconductivity and superfluidity; the OhnaKawasaki model for diblock copolymers; models of image enhancement; and MongeAmpère 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 GinzburgLandau equation

Nonlocal CahnHilliard and isoperimetric problems: Periodic phase separation induced by competing long and shortrange interactions

On a generalized GinzburgLandau energy for superconducting/normal composite materials

Global questions for map evolution equations

Pohožaevtype identities for an elliptic equation

Some remarks on MongeAmpère functions

Variational versus pdebased approaches in mathematical image processing

On the energy of a ChernSimonsHiggs 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 GrossPitaevskii energy

Bifurcation of vortex solutions to a GinzburgLandau equation in an annulus

An AllenCahn type problem with curvature modification

Rare events, action minimization, and sharp interface limits

The GaussGreen theorem for weakly differentiable vector fields