Boundary Harnack principle for Brownian motions with measure-valued drifts in bounded Lipschitz domains
The main purpose of this paper is to prove a scale invariant boundary Harnack principle in bounded Lipschitz domains, for diffusions with measure valued drifts. It is also proved that the Martin boundary and the minimal Martin boundary coincide with the Euclidean boundary. These results generalize the corresponding results of \textit{L. Caffarelli, E. Fabes, S. Mortola} and \textit{S. Salsa} [Indiana Univ. Math. J. 30, 621--640 (1981; Zbl 0512.35038)] and of \textit{E. Fabes, N. Garofalo, S. Marin-Malave} and \textit{S. Salsa} [Rev. Mat. Iberoam. 4, No.~2, 227--251 (1988; Zbl 0703.35058)].
scientific article