Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs)
"The book has two distinct parts.  The first part begins with some topics from abstract measure theory, continues with an introduction to basic geometric measure theory, and concludes with BV functions and the theory of sets of finite perimeter.  It is assumed that the reader has a basic knowledge of measure and integration theory. The second part of the book is oriented towards the study of specific variational problems." -- --Mathematical Reviews"This book provides an excellent account of the theory of BV functions (apparently for the first time in book form), and a nice introduction to geometric measure theory, as well as a rigorous survey of results for 'free discontinuity' problems modeled to the Mumford-Shah problem."--The Bulletin ofthe London Mathematical Society"The most important contribution of this book and what makes it unique is that it offers a comprehensive, unified, and self-contained treatment of contemporary BV theory that nicely complements the existing literature. ... The book also contains new contributions, such as the formula of push-forward in BV, and some proofs of known results have been greatly simplified. ... This is a book with staying power, an invaluable source for experts in the calculus of variations, geometric measure theory, and partial differential equations, and a graduate textbook for advanced Ph.D. students ..."--Societyfor Industrial and Applied Mathematics