arXiv math-ph/06120132006-12math-phmath.MP

具有快振荡系数的椭圆型方程组解的渐近性

Asymptotics for the solutions of elliptic systems with fast oscillating coefficients

Denis Borisov

备注：: I have excluded the results on the eigenvalues asymptotitcs from the article. The reason is that I've obtained the referee report and he is demanded me to do it. As a result, I shortened this preprint. The results on the eigenvalue asymptotics will be written as an independent article, and the preprint will be submitted to arXiv

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摘要：

在全空间中考虑二阶椭圆型方程组的奇摄动。系统的系数快速振荡，并依赖于慢变量和快变量。我们得到了齐次化算子，并在一致范数意义下构造了系统所描述的算子的预解式的渐近展开式的前导项。建立了谱的收敛性。建立了谱的收敛性。并给出了实例。

英文摘要：

We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense we construct the leading terms of the asymptotics expansion for the resolvent of the operator described by the system. The convergence of the spectrum is established. The convergence of the spectrum is established. The examples are given.

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