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Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.

Calculus of variations --- Functions of bounded variation --- Convergence --- Perturbation (Mathematics) --- Calcul des variations --- Convergentie --- Fonctions à variation bornée --- Functies met begrensde variatie --- Perturbatie (Wiskunde) --- Perturbation (Mathématiques) --- Variatieberekening --- Partial differential equations. --- Numerical analysis. --- Mathematical physics. --- Partial Differential Equations. --- Numerical Analysis. --- Theoretical, Mathematical and Computational Physics. --- Physical mathematics --- Physics --- Mathematical analysis --- Partial differential equations --- Mathematics --- Functions of bounded variation. --- Convergence. --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Functions --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables