Univalent solutions of an elliptic system of partial differential equations arising in homogenization
Univalent solutions of an elliptic system of partial differential equations arising in homogenization
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均质化过程中产生的偏微分方程椭圆方程组的单价解
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
V. Nesi
中科院分区：
文献类型：
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作者：
P. Bauman;A. Marini;V. Nesi
本文证明了一类散度型椭圆型偏方程组的解，其边值是二维凸域上的一次向量同构的限制，是其向量具有非负行列式的映射。在关于区域、边值和椭圆组系数的适当正则性假设下，证明了解是向量有严格位置行列式的有向同构。我们还描述了我们的结果在齐次化问题上的应用。
In this paper we prove that solutions to an elliptic system of partial diVerential equations in divergence form whose boundary values are the restriction of a diVeomorphism of de- gree one onto a convex domain in two dimensions are mappings whose diVerential has a nonnegative determinant. Under appro- priate regularity assumptions on the domain, the boundary val- ues, and the coeYcients of the elliptic system, it is shown that so- lutions are diVeomorphisms whose diVerential has a strictly pos- itive determinant. We also describe applications of our results to problems arising in homogenization.