We show the effectiveness of viscosity-solution methods in asymptotic problems for second-order elliptic partial differential equations (PDEs) with a small parameter. Our stress here is on the point that the methods, based on stability results , , apply without hard PDE calculations. We treat two examples from  and . Moreover, we generalize the results to those for Hamilton-Jacobi-Bellman equations with a small parameter.
ASJC Scopus subject areas