In this paper we give a characterization of the optimal cost of a stopping time problem as the maximum solution of a variational inequality without coercivity. Some properties of continuity for the optimal cost are also given.
Numerical Analysis and Computation
J.-L. Menaldi, On the optimal stopping time problem for degenerate diffusions, SIAM J. Control Optim., 18 (1980), pp. 697-721. doi: 10.1137/0318052