Uniform asymptotic expansion of the voltage potential in the presence of thin inhomogeneities with arbitrary conductivity

DOI10.1007/s11401-016-1072-3zbMath1368.35095OpenAlexW2568760610MaRDI QIDQ523807

Charles Dapogny, Michael S. Vogelius

Publication date: 21 April 2017

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-016-1072-3

zbMATH Keywords

Dirichlet problemuniform asymptotic expansionssecond order elliptic equationconductivity problemsthin inhomogeneities

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Inverse problems in equilibrium solid mechanics (74G75)

Related Items (5)

The topological ligament in shape optimization: a connection with thin tubular inhomogeneities ⋮ An Asymptotic Representation Formula for Scattering by Thin Tubular Structures and an Application in Inverse Scattering ⋮ A connection between topological ligaments in shape optimization and thin tubular inhomogeneities ⋮ Small perturbations in the type of boundary conditions for an elliptic operator ⋮ Extending representation formulas for boundary voltage perturbations of low volume fraction to very contrasted conductivity inhomogeneities

Cites Work

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• Asymptotic expansion of steady-state potential in a high contrast medium with a thin resistive layer
• A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity
• Reinforcement problems in the calculus of variations
• Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis.
• Reconstruction of small inhomogeneities from boundary measurements
• Variation and optimization of formes. A geometric analysis
• Shapes and Geometries
• Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction
• A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
• Reconstruction of Thin Conductivity Imperfections
• Multi-phase structural optimizationviaa level set method

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