Functions of Bounded Variation and Free Discontinuity Problems

This book presents the reader with a systematic introduction to a class of variational problems called 'free discontinuity problems'. Examples of such problems come, for instance, from fracture mechanics, image analysis, or the theory of phase transitions. The book bridges the gap between the research level and elementary courses on measure theory and calculus of variation at a level suitable for graduate students. The first half of the book contains a comprehensive and updated treatment of the theory of Functions of Bounded Variation and of the mathematical prerequisites of that theory, that is Abstract Measure Theory and Geometric Measure Theory.