Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions

2009/09/22 by Ellen Shiting Bao, Yanyan Li, Bao, Ellen ShiTing +3 · 2 citations
Computer Science · Mathematics · #35B25 #35B45 #35J25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0909.3901

openalex publication_date 2009/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in ℝⁿ, n≥ 2. For these two extreme cases of the conductivity problems, the gradients of their solutions may blow up as two inclusions approach each other. We establish the gradient estimates for the perfect conductivity problems and an upper bound of the gradients for the insulated conductivity problems in terms of the distances between any two closely spaced inclusions.

Cited by

• Optimal gradient estimates for conductivity problems with imperfect low-conductivity interfaces
• Gradient estimates for the insulated conductivity problem with partially flat inclusions

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