Estimates on the solution of an elliptic equation related to Brownian motion with drift.
In this paper we are concerned with studying the Dirichlet problem for an elliptic equation on a domain in R3. For simplicity we shall assume that the domain is a ball ΩR of radius R. Thus: ΩR = {x ∈ R3 : |x| < R}. The equation we are concerned with is given by (-Δ - b(x).∇) u(x) = f(x), x ∈ ΩR, with zero Dirichlet boundary conditions.