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

M. BRAMANTI, L. BRANDOLINI, E. HARBOURE Y B. VIVIANI.

ANNALI DI MATEMATICA PURA ED APPLICATA

SPRINGER HEIDELBERG

Año: 2011

0373-3114

In this article we give some a priori Lp(Rn) estimates for elliptic operators in non-divergence form with VMO-coeficients and a potential V  satisfying an appropriate reverse-Holder condition, generalizing previous results due to Chiarenza-Frasca-Longo to the scope of Schrodinger type operators. In particular, our class of potentials includes unbounded functions such as non-negative polynomials. We apply such a priori estimates to derive some global existence and uniqueness results under some additional assumptions on V .