Variational Methods for Discontinuous Structures, Softcover reprint of the original 1st ed. 2002 International Workshop at Villa Erba (Cernobbio), Italy, July 2001 Progress in Nonlinear Differential Equations and Their Applications Series, Vol. 51

This volume contains the Proceedings of the International Workshop Variational Methods For Discontinuous Structures, which was jointly organized by the Dipar­ timento di Matematica Francesco Brioschi of Milano Politecnico and the Interna­ tional School for Advanced Studies (SISSA) of Trieste. The Conference took place at Villa Erba Antica (Cernobbio) on the Lago di Como on July 4- 6, 2001. In past years the calculus of variations faced mainly the study of continuous structures, say particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities: in many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, varia­ tional description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes; in most cases theoretical and numerical analysis of these models were provided. viii Preface Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport prob­ lems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework.

A Model for Mixtures of Micromagnetic Materials allowing Existence and Regularity.- Variational Properties of a Model for Image Segmentation with Overlapping Regions.- Variational Theory of Weak Geometric Structures.- Optimal Transportation Problems with Free Dirichlet Regions.- Local Minimizers for a Free Gradient Discontinuity Problem in Image Segmentation.- Irrigation.- Symmetrization and Functionals Defined on BV.- Interface Energies and Structured Deformations in Plasticity.- Higher Order Variational Problems and Phase Transitions in Nonlinear Elasticity.- Unstable Crystalline Wulff Shapes in 3D.- Dimension Reduction in Continuum Mechanics.- Reaction-Diffusion Equations and Learning.- Contributors.- List of Participants.