The elliptic equation and the Cauchy problem in Cb(R N ): the uniformly elliptic case

In this chapter we consider linear elliptic and parabolic problems in Cb(R N )

associated with the differential operator A defined by

Au(x) = N∑

qij(x)Diju(x) + N∑ i=1

bi(x)Diu(x) + c(x)u(x), x ∈ R N ,

on smooth functions. We assume the following hypotheses on the coefficients of the operator A.