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

BRAMANTI MARCOS; BRANDOLINI LUCAS; HARBOURE ELEONOR; VIVIANI BEATRIZ

ANNALI DI MATEMATICA PURA ED APPLICATA

SPRINGER HEIDELBERG

Año: 2010

0373-3114

In this article we give some a priori Lp(Rn) estimates for elliptic op- erators in non-divergence form with VMO-coe¢ cients and a potential VLp(Rn) estimates for elliptic op- erators in non-divergence form with VMO-coe¢ cients and a potential VVMO-coe¢ cients 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 func- tions such as non-negative polynomials. We apply such a priori estimates to derive some global existence and uniqueness results under some addi- tional assumptions on V .V .