论文标题
加权分配方法，用于orlicz空间中抽椭圆形双OBSTACE问题的梯度估计值
Weighted distribution approach to gradient estimates for quasilinear elliptic double-obstacle problems in Orlicz spaces
论文作者
论文摘要
我们构建了一种有效的方法来处理Lorentz和Orlicz空间中一类椭圆双重问题的全球规则性估计。本文的动机来自于分数最大分布的观点的抽象结果的研究，这项工作还通过使用加权分数最大分布（WFMD）在\ cite {pn_dist}中扩展了一些规律性结果。我们进一步研究了通过分数最大算子和数据电位的弱解梯度的重点估计。此外，在论文的环境中，我们被导致对非线性问题的研究被认为是部分弱的BMO条件（在一个固定变量中可以测量，并且仅满足其余变量中局部小型BMO eminorms）。
We construct an efficient approach to deal with the global regularity estimates for a class of elliptic double-obstacle problems in Lorentz and Orlicz spaces. The motivation of this paper comes from the study on an abstract result in the viewpoint of the fractional maximal distributions and this work also extends some regularity results proved in \cite{PN_dist} by using the weighted fractional maximal distributions (WFMDs). We further investigate a pointwise estimates of the gradient of weak solutions via fractional maximal operators and Riesz potential of data. Moreover, in the setting of the paper, we are led to the study of problems with nonlinearity is supposed to be partially weak BMO condition (is measurable in one fixed variable and only satisfies locally small-BMO seminorms in the remaining variables).
