Necessary Conditions for a Domain Optimization Problem in Elliptic Boundary Value Problems

DOI10.1137/0324020zbMath0587.49023OpenAlexW1966554776MaRDI QIDQ3713041

Nobuo Fujii

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1137/0324020

zbMATH Keywords

variational equationelliptic boundary value problemnecessary conditiondomain optimization

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Control/observation systems governed by partial differential equations (93C20) Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear systems in control theory (93C10) Statistical mechanics of plasmas (82D10)

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Lower-semicontinuity in domain optimization problems ⋮ Application of the method of fundamental solutions for designing the optimal shape in heat transfer ⋮ Generalized implicit function theorems and problems with a free boundary ⋮ Stabilization and control of distributed systems with time-dependent spatial domains ⋮ Second-order necessary conditions in a domain optimization problem ⋮ Second-order necessary optimality conditions for domain optimization problems of the Neumann type ⋮ Second-order numerical method for domain optimization problems ⋮ Finite element approximation of a shape optimization problem for von karman system ⋮ Sensitivity analysis of descriptor distributed parameter systems ⋮ Measure theoretical approach for optimal shape design of a nozzle ⋮ A domain optimization problem with boundary penalty cost functional ⋮ Unnamed Item ⋮ Optimal shape design for systems governed by variational inequalities. I: Existence theory for the elliptic case ⋮ Necessary conditions for a domain optimization problem with various constraints ⋮ Second-order necessary conditions for domain optimization problems in elastic structures. I: Surface traction given as a field ⋮ Optimal shape design for systems governed by variational inequalities. III: Necessary conditions in the elliptic case

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