Uniform estimates in two periodic homogenization problems
Uniform estimates in two periodic homogenization problems
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两个周期性均质化问题中的均匀估计
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
B. Schweizer
中科院分区：
文献类型：
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作者：
B. Schweizer
我们分析了两个偏微分方程，提出了穿孔域。我们提供了一个先验估计，不依赖于穿孔的大小：一个序列的解决方案是一致有界的Sobolev空间的正规函数。第一个均匀化问题涉及的拉普拉斯和平均曲率算子与诺依曼边界条件。我们得到一致的Lipschitz估计的解决方案。将所得结果用于流体力学自由边界系统的分析。压缩迭代得到解的存在性和一致估计。关键是使用不同于通常Lp空间的函数空间。© 2000 John Wiley & Sons，Inc.
We analyze two partial differential equations that are posed on perforated domains. We provide a priori estimates that do not depend on the size of the perforation: A sequence of solutions is uniformly bounded in a Sobolev space of regular functions. The first homogenization problem concerns the Laplace and the mean-curvature operator with Neumann boundary conditions. We derive uniform Lipschitz estimates for the solutions. The result is used in the analysis of a free boundary system of fluid mechanics. A contractive iteration yields the existence of solutions and uniform estimates. The key is the use of function spaces that are different from the usual Lp-spaces. © 2000 John Wiley & Sons, Inc.