  This paper is concerned with nonlinear elliptic equations in nondivergence
form where the operator has a first order drift term which is not Lipschitz
continuous. Under this condition the equations are nonhomogeneous and
nonnegative solutions do not satisfy the classical Harnack's inequality. This
paper presents a new type of generalization of the classical Harnack's
inequality for such equations. As a corollary we obtain the optimal Harnack
type of estimate for p(x)-harmonic functions which quantifies the strong
minimum principle.
