Some properties of an elliptic periodic problem with an interfacial resistance,ZAMM - Journal of Applied Mathematics and Mechanics

当前位置： X-MOL 学术 › ZAMM › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Some properties of an elliptic periodic problem with an interfacial resistance
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2020-07-23 , DOI: 10.1002/zamm.202000065
Patrizia Donato ₁ , Rheadel Fulgencio _{1,

2}

Affiliation

In the homogenization of quasilinear elliptic problems, it is crucial for the homogenized matrix to have some kind of Lipschitz continuity in order to provide the uniqueness of the solution of the limit problem. In this paper, we prove that some estimates providing the uniqueness for a class of quasilinear problems in a periodic two‐component domain, remains valid after the homogenization process. To do that, we first prove a suitable Meyers type estimate for the periodic cell problem describing the homogenized matrix, which is posed in a two‐component cell, with a jump of the solution proportional to the flux prescribed on the interface. We also complete the study by a boundedness result for this periodic solution.

中文翻译：

具有界面阻力的椭圆周期问题的某些性质

在准线性椭圆问题的均质化中，至关重要的是，均质化矩阵具有某种Lipschitz连续性，以提供极限问题解的唯一性。在本文中，我们证明了一些估计在周期两分量域中为一类拟线性问题提供唯一性，但在均化过程之后仍然有效。为此，我们首先针对描述均质矩阵的周期单元问题证明了合适的Meyers型估计，该均质矩阵放置在两成分单元中，并且溶液的跃迁与界面上规定的通量成比例。我们还针对此周期解通过有界结果完成了研究。

更新日期：2020-07-23

点击分享查看原文

点击收藏

阅读更多本刊最新论文