Asymptotics for the solutions of elliptic systems with fast oscillating coefficients
Abstract
Description
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.
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
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