Asymptotic analysis for elliptic systems in a narrow region

Zhiwen Zhao

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arXiv · 2204.06711

Asymptotic analysis for elliptic systems in a narrow region

Zhiwen Zhao

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Abstract

This paper is concerned with investigating the asymptotic behavior of the gradients of solutions to a class of elliptic systems with general boundary data, especially covering the Lam\'{e} systems, in a narrow region. The novelty of this paper lies in finding the correction term to improve the previous gradient estimates to be a precise asymptotic formula. Through this justification, we capture all singular terms and thus give a fairly sharp characterization in terms of the singularities of the gradients.

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Zhiwen Zhao. 2022-04-14. Asymptotic analysis for elliptic systems in a narrow region. https://arxiv.org/abs/2204.06711

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