CARLESON TYPE ESTIMATES FOR SECOND ORDER ELLIPTIC EQUATIONS WITH UNBOUNDED DRIFT

摘要

We derive a Carleson type estimate for positive solutions of non-divergence second order elliptic equations Lu — a_(ij)D_(ijU) + b_iD_(iu) — 0 in a bounded domain Ω C R~N. We assume that bi € Ln(Ω) and Ω is a twisted Holder domain of order a € (1/2,1] which satisfies a weak regularity condition. We also provide an example which shows that the main result fails in general if a € (0,1/2]. Bibliography: 18 titles.