Boundary Harnack principle for second order elliptic equations with unbounded drift

We prove the boundary Harnack principle for ratios of solutions u/v of non-divergence second order elliptic equations Lu = a _ij D _ij u + b _i D _i u = 0 in a bounded domain Ω ⊂  mathbb R {mathbb R} ⁿ . We assume that b _i ∈ L ⁿ (Ω) and Ω is a twisted H?lder domain of order α ∈ (1/2, 1]. Based on this result, we derive the H?lder regularity of u/v for uniform domains. Bibliography: 27 titles.