Geometric Flows on Planar Lattices

This book introduces the reader to important concepts in modern applied analysis such as homogenization gradient flows on metric spaces geometric evolution Gamma-convergence tools applications of geometric measure theory properties of interfacial energies etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media where these concepts are introduced and elaborated in a natural and constructive way. At the same time the analysis introduces open issues of a general and fundamental nature at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.<br> <br> <p></p>