Part 1: Introduction to homogenisation and Gamma-Convergence
We will start by introducing the notion of Gamma-convergence and its main properties. We will then show how this can be applied to the study of homogenization of integral functionals. This includes, as a particular case, the homogenization of uniformly elliptic PDEs. Lecture 1: (1) The homogenisation problem; (2) Gamma-convergence - definition, main properties, examples, comparison with pointwise limit; (3) Lower semicontinuity, lower semicontinuous envelope; (4) Coercivity
Overview
Abstract
We will start by introducing the notion of Gamma-convergence and its main properties. We will then show how this can be applied to the study of homogenization of integral functionals. This includes, as a particular case, the homogenization of uniformly elliptic PDEs.
Lecture 1
- The homogenisation problem
- Gamma-convergence
- definition
- main properties
- examples
- comparison with pointwise limit
- Lower semicontinuity, lower semicontinuous envelope
- Coercivity
Brief Biography
Filippo Cagnetti got a Master degree in Physics in 2003, at University "La Sapienza" in Rome, Italy. In 2007 he obtained a Ph.D.in Applied Mathematics at SISSA, Trieste, Italy, under the supervision of Gianni Dal Maso and Massimiliano Morini. After that, he has been postdoctoral associate in the Carnegie Mellon|Portugal UT Austin|Portugal programs, spending 1 year and a half at Carnegie Mellon University, Pittsburgh, USA, 6 months at University of Texas, Austin, USA, and 3 years at Instituto Superior Tecnico, Lisbon, Portugal. In 2013, he joined the University of Sussex, where he is now Senior Lecturer in Mathematics (Mathematics, Analysis and Partial Differential Equations Research Group).
