中文摘要：

研究关于函数的非齐次A-调和方程-divA（x,u,▽u）=B（x,u,▽u）在黎曼流形测地球上弱解的Caccioppoli估计,以及它的弱逆Hlder不等式。根据散度定理和Young不等式,得到非齐次A-调和方程-divA（x,u,▽u）=B（x,u,▽u）的非负解u在完备黎曼流形上的Caccioppoli估计;根据Caccioppoli估计以及Moser迭代等方法,得到非齐次A-调和方程-divA（x,u,▽u）=B（x,u,▽u）的非负解u在测地球B（r）上的弱逆Hlder不等式。

英文摘要：

Abstract： The Caccioppoli estimates and weak reverse Holder inequalities for the weak solution to the non-homogeneous A-harmonic equation - divA （x, u, ▽ u） = B （ x, u, ▽ u） in a geodesic ball for Riemann manifolds are studied. Firstly, by using the divergence theorem and Young inequality, the Caccioppoli estimates about the nonnegative solutionuof the non-homogeneous A-harmonic equa- tion - divA （x, u, ▽ u） = B（x, u, ▽ u） on the complete Riemann manifold are obtained. Then, according to the previous Caccioppoli estimates and Moser iteration etc., the weak inverse Holder inequality about the nonnegative solution u of the nonhomogeneous A-harmonic equation - divA （x, u, ▽ u） =B（x,u, ▽ u）on a geodesic ball B（r） is given.