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arXiv · 2010.04593

Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials

Yiping Zhang
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Abstract

In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients and rapidly oscillating periodic potentials, we are interested in the $H^1$ convergence rates and the Dirichlet eigenvalues and bounds of the normal derivatives of Dirichlet eigenfunctions. The $H^1$ convergence rates rely on the Dirichlet correctors and the first-order corrector for the oscillating potentials. And the bound results rely on an $O(\varepsilon)$ estimate in $H^1$ for solutions with Dirichlet condition.

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Yiping Zhang. 2020-10-08. Estimates of eigenvalues and eigenfunctions in elliptic homogenization with rapidly oscillating potentials. https://doi.org/10.1016/j.jde.2021.05.006

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