Abstract
A generalization of Harnack's inequality is given for solutions of the differential inequality (1)in which is a uniformly elliptic operator with measurable and bounded coefficients, and are fixed positive constants, and , , is some number. It is shown that there exist , , depending on the ellipticity constant and the dimension of the space, and 1$ SRC=http://ej.iop.org/images/0025-5734/53/2/A03/tex_sm_2924_img9.gif/>, depending on the ellipticity constant, the dimension of the space and the numbers , and , such that for solutions of inequality (1) with which are positive in the ball of radius with center at the origin, and such that M_0$ SRC=http://ej.iop.org/images/0025-5734/53/2/A03/tex_sm_2924_img13.gif/>, Harnack's inequality holds if is commensurate with with the constant in Harnack's inequality depending only on the dimension of the space and the ellipticity constant.Bibliography: 9 titles.
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