摘要
本文讨论了一类具有ｐ－Ｌａｐｌａｃｅ散度头部的方程组及其对应的障碍问题的部分正则性，其中算子具有自然增长条件。应用Ｍｏｒｒｅｙ空间与Ｃａｍｐａｎａｔｏ空间的性质，我们得出如下结论：当障碍的梯度属于Ｌσ（Ω，ＲＮ）时，问题的解属于Ｃ（Ω０，ＲＮ）；当时，解的梯度属于Ｃ（Ω０，ＲａＮ），其中Ω０是Ω的开子集，ｍｅｓ（Ω＼Ω０）＝０。最后，我们对两个障碍的问题得到了类似结果。
his peper is concerned with the partial regularity of weak solutions to certain obstacleproblems involving p-Laplacian type elliptic systems with natural growth conditions. By virtue ofMoney and Campanato estimates, we conclude that the solutions belong to C(Ω0, RN ) (σ > n),andthe gradient of the weak solution belongS to Cfor some 0< β < 1 where 1 <ρ < ∞,mes(Ω/Ω0) = 0. In the final section we have got similar conclusionsfor double obstacle problems.
关键词
障碍问题
部分正则性
向量值
p-Laplac elliptic systems
obstacle problems
partial regularity
