One of the most powerful tools
in studying second order elliptic and parabolic differential equations is the barrier
method, i.e. using the comparison principle with a suitable comparison or
barrier function to infer some feature of the boundary behavior of a solution
to such an equation. For sufficiently smooth domains Ω (e.g. ∂Ω ∈ C2),
barrier functions can be constructed rather easily in terms of the distance
function d(x) =dist(x,∂Ω) because d is a C2 function near ∂Ω; for less smooth
domains it need not be even C1 (although it is Lipschitz continuous.) These
less smooth domains are of interest and several authors have constructed
barriers for certain such domains. We consider here a general method for
constructing these barriers by introducing a regularized distance, described
below.
