Journal article
Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains
- Abstract:
- We study parabolic Hamilton-Jacobi-Bellman (HJB) equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the problem to obtain well-posedness and regularity of a related switching system and the convergence of its components to the HJB equation. In particular, we show existence of a viscosity solution to the switching system by a novel construction of sub- and supersolutions and application of Perron's method. Error bounds for monotone schemes for the HJB equation are then derived from estimates near the boundary, where the standard regularisation procedure for viscosity solutions is not applicable, and are found to be of the same order as known results for the whole space. We deduce error bounds for some common finite difference and truncated semi-Lagrangian schemes.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 407.5KB, Terms of use)
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- Publisher copy:
- 10.1016/j.jde.2019.11.081
Authors
- Publisher:
- Elsevier
- Journal:
- Journal of Differential Equations More from this journal
- Volume:
- 268
- Issue:
- 12
- Pages:
- 7843-7876
- Publication date:
- 2019-12-05
- Acceptance date:
- 2019-11-20
- DOI:
- ISSN:
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0022-0396
- Language:
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English
- Keywords:
- Pubs id:
-
pubs:1073124
- UUID:
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uuid:5efbb6cb-a81d-4a7c-bcbe-fc6254a58457
- Local pid:
-
pubs:1073124
- Source identifiers:
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1073124
- Deposit date:
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2019-11-20
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier Inc
- Copyright date:
- 2019
- Rights statement:
- © 2019 Elsevier Inc. All rights reserved.
- Notes:
-
This is the accepted manuscript version of the article. The final version is available from Elsevier at https://doi.org/10.1016/j.jde.2019.11.081
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