Book (Cambridge University Press)
Inserted: 9 may 2022
Last Updated: 7 apr 2023
The object of the analysis in this book are energies whose domain are functions defined on a lattice $\cal L$ in $\mathbb R^d$, or a portion of that lattice, and whose values are taken in a finite set $Y$ as the lattice is scaled so that the lattice size tends to $0$. The abundance of techniques and results directly obtained for such types of energies, or for problems where these energies are part of the description, has stimulated the need of a systematization both for an unitary formal structure and in order to highlight in a clear way completely novel directions both applied and theoretical, such as links with Discrete Dynamical Systems and Graph Theory. The book wants to be a proposal for the formalization of a common language both within the rich and various subject of Variational Methods, and towards quite different lines of research, which are essentially discrete. The choice of focussing on discrete interfacial energies is due to the ease of expressing in their terms problems that are intrinsically discrete and not only a discretization of a continuous analog, and at the same time to the generality of the methods and results, which can be exported to problems with other scalings and physical interpretations.