Thin Structures, Homogenization and Multi Phase Problems*

Start Date: 2011 End Date:: 2014
PIs: Luísa Mascarenhas (FCT/UNL) and Giovani Leoni (CMU)
Team: Fundação da Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa (FFCT/FCT/UNL), Carnegie Mellon University (CMU)

Abstract:
This proposal reflects a long history of scientific collaboration between members of the Portuguese partner institutions and those of CMU. Through this project these existing synergies will continue to be further developed and enhanced, bringing in CMU´s high-level scientific research and training experience. This project also includes a CMU|Portugal Ph.D. student and two CMU|Portugal postdoctoral fellows. Below we list the research subjects to be addressed. These topics share the commonality of the techniques used in Nonlinear Analysis and in Calculus of Variations, and are contemporary pieces of an ambitious research program that brings in forefront techniques in these fields to address pressing issues in material science and in image processing.
    I. Thin structures: dimension reduction and eigenvalue problems; bending, no locality and linear growth asymptotic; mathematical models for thin structures in a BV setting.
    II. Homogenization and multi-phase problems: relaxation of first and second order problems with linear growth; relaxation and homogenization of functional in image segmentation models; variational problems with volume constraints; homogenization in multi-phase and multicomponent systems; homogenization in multi-phase and multi-component systems.

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*Project approved in the Call 2009 in Applications of Mathematics Thematic Areas, in the framework of the Carnegie Mellon Portugal Program and UT Austin-Portugal