Convergence results for Hamilton-Jacobi-Bellman equations in variable domains (Q1198703)

The paper deals with the stability of Hamiton-Jacobi problems in Dirichlet form \[ \begin{cases} u+H\bigl(x,u,Du\bigr)=0 &\text{in }\Omega\\ u=g &\text{on }\partial\Omega,\end{cases} \] with respect to perturbations of the Hamiltonian \(H\), the domain \(\Omega\), and the initial datum \(g\). The results of this paper improve previous ones of the authors [Appl. Math. Optimization 24, No. 2, 113-128 (1991; Zbl 0745.49024)], where only \(H\) was perturbed. The paper takes advantage of a new comparison technique of \textit{M. C. Crandall, H. Ishii} and \textit{P. L. Lions} [J. Math. Soc. Japan 39, 581-596 (1987; Zbl 0644.35016)].