Gorny W., Mazon J. Functions of Least Gradient 2024

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