Partial Differential Equations and Monge-Kantorovich Mass Transfer

Heuristics 2.1 Geometry of optimal transport 2.2 Lagrange multipliers 3. Optimal mass transport, polar factorization 3.1 Solution of dual problem 3.2 Existence of optimal mass transfer plan 3.3 Polar factorization of vector fields 4. Regularity 4.1 Solving the Monge–Ampere equation 4.2 Examples 4.3 Interior regularity for convex targets 4.4 Boundary regularity for convex domain and target 5. Application: Nonlinear interpolation 6. Application: Time-step minimization and nonlinear diffusion 6.1 Discrete time approximation 6.2 Euler–Lagrange equation