2016/06/09 by Hongjie Dong, Haigang Li, Dong, Hongjie +1 · 4 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1606.02793
openalex publication_date 2016/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a class of second-order elliptic equations of divergence form, with discontinuous coefficients and data, which models the conductivity problem in composite materials. We establish optimal gradient estimates by showing the explicit dependence of the elliptic coefficients and the distance between interfacial boundaries of inclusions. The novelty of these estimates is that they unify the known results in the literature and answer open problem (b) proposed by Li-Vogelius (2000) for the isotropic conductivity problem. We also obtain more interesting higher-order derivative estimates, which answers open problem (c) of Li-Vogelius (2000). It is worth pointing out that the equations under consideration in this paper are nonhomogeneous.