On the notion of boundary conditions in comparison principles for viscosity solutions

Abstract : We collect examples of boundary-value problems of Dirichlet and Dirichlet–Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear elliptic partial differential equations. In particular, our model problem is the Monge–Ampère equation, which is treated through its equivalent reformulation as a Hamilton–Jacobi–Bellman equation. Our examples illustrate how the different notions of boundary conditions appearing in the literature may admit different sets of viscosity sub-and supersolutions. We then discuss how these examples relate to the validity of comparison principles for these different notions of boundary conditions.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

https://hal.inria.fr/hal-01493586
Contributeur : Iain Smears <>
Soumis le : mardi 21 mars 2017 - 18:08:56
Dernière modification le : jeudi 26 avril 2018 - 10:28:41
Document(s) archivé(s) le : jeudi 22 juin 2017 - 14:08:31

Fichier

monge_ampere.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01493586, version 1

Collections

Citation

Max Jensen, Iain Smears. On the notion of boundary conditions in comparison principles for viscosity solutions. 2017. 〈hal-01493586〉

Partager

Métriques

Consultations de la notice

316

Téléchargements de fichiers

33