Jensen, Max;
Smears, Iain;
(2018)
On The Notion Of Boundary Conditions In Comparison Principles For Viscosity Solutions.
In: Kalise, Dante and Kunisch, Karl and Rao, Zhiping, (eds.)
Numerical Methods and Applications in Optimal Control.
De Gruyter
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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.
| Type: | Book chapter |
|---|---|
| Title: | On The Notion Of Boundary Conditions In Comparison Principles For Viscosity Solutions |
| ISBN-13: | 9783110542639 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/9783110543599 |
| Publisher version: | https://doi.org/10.1515/9783110543599 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| Keywords: | Viscosity boundary conditions, comparison principles, Hamilton–Jacobi– Bellman equations, Monge–Ampère equations, Barles–Souganidis theorem |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10156977 |
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