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arXiv · 1902.10332

Oscillatory integrals and periodic homogenization of Robin boundary value problems

Jun Geng·Jinping Zhuge
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Abstract

In this paper, we consider a family of second-order elliptic systems subject to a periodically oscillating Robin boundary condition. We establish the qualitative homogenization theorem on any Lipschitz domains satisfying a non-resonance condition. We also use the quantitative estimates of oscillatory integrals to obtain the dimension-dependent convergence rates in $L^2$, assuming that the domain is smooth and strictly convex.

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Jun Geng, Jinping Zhuge. 2019-02-27. Oscillatory integrals and periodic homogenization of Robin boundary value problems. https://arxiv.org/abs/1902.10332

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