Let v ? C(Rn). We say that v is a viscosity subsolution (supersolution) to the stationary obstacle..

Let v ∈
C(Rn). We say that v is a viscosity subsolution (supersolution) to the stationary
obstacle problem if, for all u ∈
C2(Rn) such that v − u has a global max (min) at x0 ∈ Rn and u(x0) = v(x0),
then

                         min{−Lu(x0) + c(x0)u(x0)
− f (x0), u(x0) − ϕ(x0)} ≤ (≥) 0. (3.3)

We say that v is a viscosity solution if it is both a sub-
and supersolution.