Geometric Partial Differential Equations proceedings

✍ Scribed by Nicholas D. Alikakos (auth.), Antonin Chambolle, Matteo Novaga, Enrico Valdinoci (eds.)

• Publisher: Edizioni della Normale
• Year: 2013
• Tongue: English
• Leaves: 276
• Series: CRM Series 15
• Edition: 1
• Category: Library

✦ Synopsis

This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

✦ Table of Contents

Front Matter....Pages i-xiii
On the structure of phase transition maps for three or more coexisting phases....Pages 1-31
The nonlinear multidomain model: a new formal asymptotic analysis....Pages 33-74
Existence and qualitative properties of isoperimetric sets in periodic media....Pages 75-92
Minimizing movements and level set approaches to nonlocal variational geometric flows....Pages 93-104
Homogenization with oscillatory Neumann boundary data in general domain....Pages 105-118
The analysis of shock formation in 3-dimensional fluids....Pages 119-138
Regularity of the extremal solutions for the Liouville system....Pages 139-144
On general existence results for one-dimensional singular diffusion equations with spatially inhomogeneous driving force....Pages 145-170
On representation of boundary integrals involving the mean curvature for mean-convex domains....Pages 171-187
Boundary regularity for the Poisson equation in reifenberg-flat domains....Pages 189-209
Limiting models in condensed matter Physics and gradient flows of 1-homogeneous functional....Pages 211-226
Maximally localized Wannier functions: existence and exponential localization....Pages 227-250
Flows by powers of centro-affine curvature....Pages 251-265
Back Matter....Pages 267-268

✦ Subjects

Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization