Gamma-Convergence for Beginners (Relié)

The theory of gamma-convergence is-commonly recognised as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from image processing to fracture mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of convergence and at the same time provide a stimulating starting point for further studies.
The main part is set in a one-dimensional framework that allows the main issues of convergence to be highlighted without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, and free-discontinuity problems and their discrete and continuous approximation.
The author makes stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of convergence illustrated in the previous section maybe applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of applied analysis, and from interactions with many specialists in mechanics and computer vision, which have helped in making the text accessible to a non-mathematical audience.
The material in the book is almost self-contained, requiring only some basic notion of measure theory and functional analysis.