Global H\"{o}lder solvability of second order elliptic equations with locally integrable lower-order coefficients

Abstract

We prove the existence of globally H\"{o}lder continuous solutions to certain elliptic partial differential equations with lower-order terms. Our result is applicable to coefficients controlled by a negative power of the distance from the boundary of the domain and significantly improves Theorem 8.30 in Gilbarg and Trudinger (1983). The proof is derived by applying the strategy of Ancona (1986) to a new Morrey-type space.