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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 SmearsWe 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.
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Publication status
- Published
File Version
- Published version
Journal
Hamilton-Jacobi-Bellman EquationsPublisher
De GruyterExternal DOI
Page range
143-154Pages
198.0Event name
Numerical methods for Hamilton-Jacobi equations in optimal control and related fieldsEvent location
Johann Radon Institute for Computational and Applied Mathematics, Linz, AustriaEvent type
workshopEvent date
21-25 November 2016Book title
Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal ControlPlace of publication
BerlinISBN
9783110543599Series
Radon Series on Computational and Applied MathematicsDepartment 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 RaoLegacy Posted Date
2018-02-20First Open Access (FOA) Date
2019-08-01First Compliant Deposit (FCD) Date
2018-02-20Usage metrics
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