ABSTRACT
In this chapter we deal with the problem of the uniqueness of the solution of the elliptic equation
λv(x) −Av(x) = f(x), x ∈ RN , (4.0.1)
(f ∈ Cb(RN )) which belongs to
Dmax(A) =
{ u ∈ Cb(R
N ) ∩ ⋂
W 2,ploc (R N ) : Au ∈ Cb(R
N )
} , (4.0.2)
and of the solution to the parabolic problem{ Dtu(t, x)−Au(t, x) = 0, t > 0, x ∈ RN ,
u(0, x) = f(x), x ∈ RN , (4.0.3)
which belongs to C([0,+∞) × RN ) ∩ C1,2((0,+∞) × RN ) and it is bounded in [0, T ]× RN for any T > 0. Throughout the chapter, we assume that the hypotheses of Chapter 2 are
satisfied. For the reader’s convenience, we state them again.
