Asymptotic analysis for elliptic systems in a narrow region

2022/04/14 by Zhao, Zhiwen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.06711

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 Lamé 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.

Related

• Derivative estimates of solutions of elliptic systems in narrow regions
• Estimates for Elliptic Systems in a Narrow Region arising from Composite Materials
• Gradient estimates for elliptic systems from composite materials with closely spaced stiff C^1,γ inclusions
• Up-to-boundary pointwise gradient estimates for very singular quasilinear elliptic equations with mixed data
• Gradient asymptotics of solutions to the Lamé systems in the presence of two nearly touching C^1,γ-inclusions in all dimensions