Global W 2,p estimates for nondivergence elliptic operators with potentials satisfying a reverse Hölder condition

Abstract

In this article, we give some a priori L p(ℝ n) estimates for elliptic operators in nondivergence form with VMO coefficients and a potential V satisfying an appropriate reverse Hölder condition, generalizing previous results due to Chiarenza-Frasca-Longo to the scope of Schrödinger-type operators. In particular, our class of potentials includes unbounded functions such as nonnegative polynomials. We apply such a priori estimates to derive some global existence and uniqueness results under some additional assumptions on V.