论文标题
内饰$ l_ {p} $ for Stokes Systems
Interior $L_{p}$ regularity for Stokes systems
论文作者
论文摘要
一种新的迭代方法代表了研究内部$ l_ {p} $ divergence Systems的内部$ l_ {p} $，均以发散形式和非差异形式。通过迭代，我们逐步提高了解决Stokes系统解决方案的衍生物的整合性；在无限多步骤之后，实现了$ l_ {p} $规律性；在每个步骤中，使用最大函数方法，其中解决方案及其衍生物在每个尺度中同时涉及。假定空间变量中系数的Hölder连续性可以补偿溶液及其衍生物之间的不同尺度。
A new iteration method is represented to study the interior $L_{p}$ regularity for Stokes systems both in divergence form and in non-divergence form. By the iteration, we improve the integrability of derivatives of solutions for Stokes systems step by step; after infinitely many steps, $L_{p}$ regularity is achieved; and in each step, the maximal function method is used where solutions and their derivatives are involved simultaneously in each scale. The Hölder continuity of the coefficients in spatial variables is assumed to compensate the different scalings between the solutions and their derivatives.
