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. In: Kalise, Dante, Kunisch, Karl and Rao, Zhiping (eds.) Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control. Radon Series on Computational and Applied Mathematics . De Gruyter, Berlin, pp. 143-154. ISBN 9783110543599 (Accepted)

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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 application of comparison principles in the analysis of numerical methods.

Item Type: Book Section
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
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Depositing User: Max Jensen
Date Deposited: 20 Feb 2018 13:07
Last Modified: 17 Aug 2018 07:56
URI: http://sro.sussex.ac.uk/id/eprint/73726

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