  In this paper we first study the penalization approximation of stochastic
differential equations reflected in a domain which satisfies conditions (A) and
(B) and prove that the sequence of solutions of the penalizing equations
converges in the uniform topology to the solution of the corresponding
reflected stochastic differential equation. Then by using this convergence
result, we consider partial differential equations with Neumann boundary
conditions in domains neither smooth nor convex and prove the existence and
comparison principle of viscosity solutions of such nonlinear PDEs. Also, by
applying the support of reflected diffusions established in \cite{ren-wuAP}, we
establish the maximum principle for the viscosity solutions of linear PDEs with
Neumann boundary conditions.
