Singularities in PDE and the Calculus of VariationsStanley Alama, Lia Bronsard, Peter J. Sternberg American Mathematical Soc. - 267 páginas 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. |
Contenido
| 1 | |
On the Cauchy Problem for Phase and Vortices in the Parabolic Ginzburg Landau Equation | 11 |
Periodic Phase Separation Induced by Competing Long and ShortRange Interactions | 33 |
On a Generalized Ginzburg Landau Energy for SuperconductingNormal Composite Materials | 47 |
Global Questions for Map Evolution Equations | 61 |
PohožaevType Identities for an Elliptic Equation | 75 |
Some Remarks on Monge Ampère Functions | 89 |
Variational Versus PDEBased Approaches in Mathematical Image Processing | 113 |
Some Recent Results about a Class of Singularly Perturbed Elliptic Equations | 153 |
The Dipole Problem for H12S2S1Maps and Application | 165 |
Hodge Decompositions 𝛤Convergence and the Gross Pitaevskii Energy | 179 |
Bifurcation of Vortex Solutions to a GinzburgLandau Equation in an Annulus | 187 |
An Allen Cahn Type Problem with Curvature Modification | 201 |
Rare Events Action Minimization and Sharp Interface Limits | 217 |
The Gauss Green Theorem for Weakly Differentiable Vector Fields | 233 |
On the Energy of a Chern Simons Higgs Vortex Lattice | 127 |
Términos y frases comunes
Ampère functions Anal approximation asymptotic bifurcation boundary conditions Comm compact consider constant convergence convex D²u defined denote diblock copolymer dimension div F domain dynamics E-mail address eigenfunction eigenvalue energy estimates exists finite perimeter Ginzburg Ginzburg-Landau harmonic map heat equation implies integral Jacobian Landau Lemma linear lower bound magnetic field Math Mathematical Mathematics Subject Classification mean curvature minimizers mn/ms Monge Monge-Ampère functions Neumann problem nonlinear nonlinear Schrödinger equations nonlocal normal trace obtain parameter Partial Differential Equations phase Phys problem proof Proposition prove Pure Appl radial Radon measure result satisfies scale Section sequence set of finite sharp interface singularities smooth functions solution space superconductivity T-convergence term Theorem theory topology variation vector field vortex vortices zero ди
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