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

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posted on 2023-06-09, 12:16 authored by Max Jensen, Iain Smears
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–Ampe`re 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 application of comparison principles in the analysis of numerical methods.

History

Publication status

  • Published

File Version

  • Published version

Journal

Hamilton-Jacobi-Bellman Equations

Publisher

De Gruyter

Page range

143-154

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

Dante Kalise, Karl Kunisch, Zhiping Rao

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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