Classical Optimal Design in Two-Phase Conductivity Problems

DOI10.1137/15M1049749zbMath1346.49029OpenAlexW2513190501MaRDI QIDQ2818185

Marko Vrdoljak

Publication date: 6 September 2016

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1049749

zbMATH Keywords

optimality conditionshomogenizationrelaxationminimax problemsaddle pointoptimal designstationary diffusiontwo-phase conductivity problems

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Existence of solutions for minimax problems (49J35) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20) Optimality conditions for minimax problems (49K35) Homogenization for problems in thermodynamics and heat transfer (80M40)

Related Items (8)

A quasi-Newton method in shape optimization for a transmission problem ⋮ Exact solutions in optimal design problems for stationary diffusion equation ⋮ On the effective properties of composite elastic plate ⋮ Minimization of the elliptic higher eigenvalues for multiphase anisotropic conductors ⋮ Convergence of the optimality criteria method for multiple state optimal design problems ⋮ On unique solutions of multiple-state optimal design problems on an annulus ⋮ Optimization of the principal eigenvalue for elliptic operators ⋮ Classical optimal designs on annulus and numerical approximations

Cites Work

• A nonstandard free boundary problem arising in the shape optimization of thin torsion rods
• On Hashin-Shtrikman bounds for mixtures of two isotropic materials
• Sequential laminates in multiple-state optimal design problems
• Gradient methods for multiple state optimal design problems
• Numerical study of a relaxed variational problem from optimal design
• Regularization of optimal design problems for bars and plates. II
• Some smoothness results for the optimal design of a two-composite material which minimizes the energy
• Homogenisation theory for Friedrichs systems
• Smoothness Properties for the Optimal Mixture of Two Isotropic Materials: The Compliance and Eigenvalue Problems
• Minimization of the Ground State for Two Phase Conductors in Low Contrast Regime
• Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
• An Example of a Max-Min Problem in Partial Differential Equations
• Shape optimization by the homogenization method
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Classical Optimal Design in Two-Phase Conductivity Problems