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Estimates on the solution of an elliptic equation related to Brownian motion with drift.

Joseph G. ConlonJuan Redondo — 1995

Revista Matemática Iberoamericana

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.

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