中文摘要：

立用Hodge分解定理，得到了非齐次A-调和方程-div（A（x,Du（x）））=f（x,u（x））对应的障碍问题很弱解的局部和全局的W1,q（Ω）-正则性，其中，A（x,Du（x）））=f（x,u（x））满足文中所给的条件，从而推广了相关文献中的有关结果．该结果在优化控制问题中有着广泛的应用．

英文摘要：

Abstract： Using Hodge decomposition theorem, the local and the global wl,q（Ω）-regularity results for very weak solutions to the obstacle problems associated with the following non- homogeneous A-harmonic equations-div（A（x,Du（x）））=f（x,u（x））are obtained under certain conditions on A （x,Du（x）））=f（x,u（x））listed in the context. Theresults generalize the corresponding results in related literatures. The results can be widely applied to optimal control problems.