Abstract

An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.

中文翻译：

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增加了 Poisson 方程 Zaremba 问题解的梯度的可积性

摘要

在具有 Lipschitz 边界和快速交替的 Dirichlet 和 Neumann 边界条件的有界平面域中，Zaremba 问题的解的梯度增加的可积分性得到了一个估计值，增加的可积分性指数与边界条件变化的频率无关.