Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Picarelli, Athena¹  Reisinger, Christoph²  Arto, Julen Rotaetxe² 

[1] Univ Verona, Via Cantarane, I-37129 Verona, Italy

[2] Univ Oxford, Math Inst, Woodstock Rd, Oxford OX2 6GG, England

关键词: Parabolic Hamilton-Jacobi-Bellman equations;    Switching systems;    Viscosity solutions;    Perron's method;    Monotone schemes;    Error bounds;   

DOI  :  10.1016/j.jde.2019.11.081

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free