\(L^{\infty}\)-error estimate for a system of elliptic quasi-variational inequalities with noncoercive operators (Q1827158)

The considered system plays a fundamental role in solving Hamilton-Jacobi-Bellman equations of stochastic control problems. The coercive case was investigated by \textit{M. Boulbrachene} and \textit{M. Haiour} [ibid. 41, 993--1007 (2001; Zbl 0988.65092)]. The results are extended now to the noncoercive case. The finite element method is used and the corresponding \(L^{\infty}\)-error is obtained. The approach is different to the one for the coercive case. It is based to the \(L^{\infty}\)-stability of the solution with respect to the right-hand side and its characterization as the least upper bound of the set of subsolutions.