"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-Ampere 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."--Jacket.
Series Statement
CRM proceedings & lecture notes, 1065-8580 ; v. 44
Variational Problems Arising in Biology / Elena Alvarez-Buylla, Mariana Benitez, Alvaro Chaos, Yuriria Cortes, Gerardo Escalera-Santos, Carlos Espinosa and Pablo Padilla -- On the Cauchy Problem for Phase and Vortices in the Parabolic Ginzburg-Landau Equation / Fabrice Bethuel, Giandomenico Orlandi and Didier Smets -- Nonlocal Cahn -- Hilliard and Isoperimetric Problems: Periodic Phase Separation Induced by Competing Long- and Short-Range Interactions / Rustum Choksi -- On a Generalized Ginzburg- Landau Energy for Superconducting/Normal Composite Materials / Tiziana Giorgi and Hala Jadallah -- Global Questions for Map Evolution Equations / Meijiao Guan, Stephen Gustafson, Kyungkeun Kang and Tai-Peng Tsai -- Pohozaev-Type Identities for an Elliptic Equation / Radu Ignat -- Some Remarks on Monge-vAmpere Functions / Robert L. Jerrard -- Variational Versus PDE-Based Approaches in Mathematical Image Processing / B. Kawohl -- On the Energy of a Chern -- Simons -- Higgs Vortex Lattice / Matthias Kurzke and Daniel Spirn -- Some Recent Results about a Class of Singularly Perturbed Elliptic Equations / Andrea Malchiodi -- The Dipole Problem for H[superscript 1/2](S[superscript 2]; S[superscript 1]) -- Maps and Application / Vincent Millot -- Hodge Decompositions, r-Convergence and the Gross-Pitaevskii Energy / Alberto Montero -- Bifurcation of Vortex Solutions to a Ginzburg-Landau Equation in an Annulus / Yoshihisa Morita -- An Allen-Cahn Type Problem with Curvature Modification / Xiaofeng Ren -- Rare Events, Action Minimization, and Sharp Interface Limits / Maria G. Westdickenberg -- The Gauss-Green Theorem for Weakly Differentiable Vector Fields / William P. Ziemer.