• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

A viscosity framework for computing Pogorelov solutions of the Monge-Ampere equation

Thumbnail
View/Open
1407.1300.pdf (2.047Mb)
Date
2014
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
2014
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Dewey
Analyse
Sujet
optimal transportation; Monge-Ampere equation; Aleksandrov solutions; viscosity solutions; finite difference methods
URI
https://basepub.dauphine.fr/handle/123456789/18736
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Benamou, Jean-David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Froese, Brittany D.
118885 Departement of Mathematics [Austin]
Type
Document de travail / Working paper
Item number of pages
24
Abstract (EN)
We consider the Monge-Kantorovich optimal transportation problem between two measures, one of which is a weighted sum of Diracs. This problem is traditionally solved using expensive geometric methods. It can also be reformulated as an elliptic partial differential equation known as the Monge-Ampere equation. However, existing numerical methods for this non-linear PDE require the measures to have finite density. We introduce a new formulation that couples the viscosity and Aleksandrov solution definitions and show that it is equivalent to the original problem. Moreover, we describe a local reformulation of the subgradient measure at the Diracs, which makes use of one-sided directional derivatives. This leads to a consistent, monotone discretisation of the equation. Computational results demonstrate the correctness of this scheme when methods designed for conventional viscosity solutions fail.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.