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

Jensen, Max and Smears, Iain (2018) On the notion of boundary conditions in comparison principles for viscosity solutions. Numerical methods for Hamilton-Jacobi equations in optimal control and related fields, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, 21-25 November 2016. Published in: Kalise, Dante, Kunisch, Karl and Rao, Zhiping, (eds.) Hamilton-Jacobi-Bellman Equations. De Gruyter ISBN 9783110543599 (Accepted)

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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 application of comparison principles in the analysis of numerical methods.

Item Type: Conference Proceedings
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 20 Feb 2018 13:07
Last Modified: 21 Feb 2018 16:36
URI: http://sro.sussex.ac.uk/id/eprint/73726

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