Volume 29, 2023
|Number of page(s)||38|
|Published online||19 January 2023|
A general comparison principle for Hamilton Jacobi Bellman equations on stratified domains
UMA, ENSTA Paris, Institut Polytechnique de Paris,
2 Normandie Univ, INSA Rouen Normandie, Laboratoire LMI, 76000 Rouen, France
* Corresponding author: firstname.lastname@example.org
Accepted: 20 December 2022
This manuscript aims to study finite horizon, first order Hamilton Jacobi Bellman equations on stratified domains. This problem is related to optimal control problems with discontinuous dynamics. We use nonsmooth analysis techniques to derive a strong comparison principle as in the classical theory and deduce that the value function is the unique viscosity solution. Furthermore, we prove some stability results of the Hamilton Jacobi Bellman equation. Finally, we establish a general convergence result for monotone numerical schemes in the stratified case.
Mathematics Subject Classification: 49J53 / 35F21 / 49L25
Key words: Nonsmooth analysis / invariance principles / viscosity theory / Hamilton Jacobi equations
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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