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 \({L^{p}(\mathbb{R}^{n})}\) 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.