Singularities in PDE and the Calculus of Variations ( CRM Proceedings & Lecture Notes )

Publication series ：CRM Proceedings & Lecture Notes

Author： Stanley Alama;Lia Bronsard;Peter J. Sternberg  

Publisher： American Mathematical Society‎

Publication year： 2017

E-ISBN: 9781470439583

P-ISBN(Paperback): 9780821843505

Subject： O175.2 Partial Differential Equations

Keyword： 暂无分类

Language： ENG

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Singularities in PDE and the Calculus of Variations

Description

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.

Chapter

Cover

Title page

Contents

Preface

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}(𝕊²;𝕊¹)-maps and application

Hodge decompositions, Γ-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

Back Cover

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