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This paper uses both the maximum principle and coupling method to study gradient estimates of positive solutions to Lu = 0 on Rd, where
with (aij) uniformly positive definite and aij,bi € C1(Rd). We obtain some upper bounds of |∇u|/u and ∥∇u∥∞/∥u∥∞, which imply a Harnack inequality and improve the corresponding results proved in Cranston [4]. Besides, two examples show that our estimates can be sharp.
