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Numerical solution of the simple Monge–Ampe`re equation with nonconvex dirichlet data on non-convex domains

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posted on 2023-06-09, 12:15 authored by Max Jensen
The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Ampere equation is known independently of the convexity of the domain or Dirichlet boundary data - when the Monge-Ampere equation is posed as a Bellman problem. However, the convergence to the viscosity solution has only been proved on strictly convex domains. In this paper, we provide numerical evidence that convergence of numerical solutions is observed more generally without convexity assumptions. We illustrate how in the limit multivalued functions may be approximated to satisfy the Dirichlet conditions on the boundary as well as local convexity in the interior of the domain

History

Publication status

  • Published

File Version

  • Published version

Journal

Hamilton-Jacobi-Bellman Equations

Publisher

De Gruyter

Page range

129-142

Pages

198.0

Event name

Numerical methods for Hamilton-Jacobi equations in optimal control and related fields

Event location

Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria

Event type

workshop

Event date

21-25 November 2016

Book title

Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control

Place of publication

Berlin,

ISBN

9783110543599

Series

Radon Series on Computational and Applied Mathematics

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Editors

Kalise Dante, Karl Kunisch, Rao Zhiping

Legacy Posted Date

2018-02-20

First Open Access (FOA) Date

2019-08-01

First Compliant Deposit (FCD) Date

2018-02-20

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