Textbook in PDF format

Stands out as the first book on least gradient functions Presents both classic and new results on this topic Features open problems Preface Basic Notation Least Gradient Problem and Minimal Surfaces Existence and Characterization of Weak Solutions Anisotropic Least Gradient Problem Duality Approach Existence of Solutions in the Trace Sense Uniqueness and Structure of Solutions Regularity of Solutions Nonstandard Boundary Conditions Equivalence with an Optimal Transport Problem in Two Dimensions Applications of Optimal Transport Techniques Approximation by Nonlocal Problems Least Gradient Functions in the Metric Setting Functions of Bounded Variation and Anzellotti Pairings Basic Properties of Area-Minimizing Sets Convex Optimization Optimal Transport Problem BV Functions in Metric Random Walk Spaces and Metric Measure Spaces Index