2019/03/11 by Richard C. Kraaij, Kraaij, Richard C.
Computer Science · Economics, Econometrics and Finance · Mathematics · #47H20 #49J45 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Biology Tumor Growth #Optimization and Variational Analysis #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1903.04196
openalex publication_date 2019/03/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We extend the Barles-Perthame procedure of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f - lambda H f = h. The convergence result allows for equations on a `converging sequence of spaces' as well as Hamilton-equations written in terms of two equations in terms of operators H_† and H_† that serve as natural upper and lower bounds for the `true' operator H. In the process, we establish a strong relation between non-linear pseudo-resolvents and viscosity solutions of Hamilton-Jacobi equations. As a consequence we derive a convergence result for non-linear semigroups.