2012/08/23 by Jean‐David Benamou, Benamou, Jean-David, Brittany D. Froese +3
Mathematics · #35J96 #49M25 #65l12 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1208.4873
openalex publication_date 2012/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as applications in diverse areas. Numerical solution techniques for the OT problem remain underdeveloped. The solution is obtained by solving the second boundary value problem for the MA equation, a fully nonlinear elliptic partial differential equation (PDE). Instead of standard boundary conditions the problem has global state constraints. These are reformulated as a tractable local PDE. We give a proof of convergence of the numerical method, using the theory of viscosity solutions. Details of the implementation and a fast solution method are provided in the companion paper arXiv:1208.4870.