Global Hölder solvability of second order elliptic equations with locally integrable lower-order coefficients

We prove the existence of globally Hölder 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 [Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001]. The proof is derived by applying the strategy of Ancona [J. London Math. Soc. (2) 34 (1986), pp. 274–290] to a new Morrey-type space.