Singularities in PDE and the calculus of variations
著者
書誌事項
Singularities in PDE and the calculus of variations
（CRM proceedings & lecture notes, v. 44）
American Mathematical Society, c2008
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
- Variational problems arising in biology by E. R. Alvarez-Buylla, M. Benitez, A. Chaos, Y. Cortes, G. Escalera-Santos, C. Espinosa, and P. Padilla On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation by F. Bethuel, G. Orlandi, and D. Smets Nonlocal Cahn-Hilliard and isoperimetric problems: Periodic phase separation induced by competing long- and short-range interactions by R. Choksi On a generalized Ginzburg-Landau energy for superconducting/normal composite materials by T. Giorgi and H. Jadallah Global questions for map evolution equations by M. Guan, S. Gustafson, K. Kang, and T.-P. Tsai Pohozaev-type identities for an elliptic equation by R. Ignat Some remarks on Monge-Ampere functions by R. L. Jerrard Variational versus pde-based approaches in mathematical image processing by B. Kawohl On the energy of a Chern-Simons-Higgs vortex lattice by M. Kurzke and D. Spirn Some recent results about a class of singularly perturbed elliptic equations by A. Malchiodi The dipole problem for $H^{1/2}(\mathbb{S}^2
- \mathbb{S}^1)$-maps and application by V. Millot Hodge decompositions, $\Gamma$-convergence and the Gross-Pitaevskii energy by A. Montero Bifurcation of vortex solutions to a Ginzburg-Landau equation in an annulus by Y. Morita An Allen-Cahn type problem with curvature modification by X. Ren Rare events, action minimization, and sharp interface limits by M. G. Westdickenberg The Gauss-Green theorem for weakly differentiable vector fields by W. P. Ziemer.
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