Optimal shape design for systems governed by variational inequalities. I: Existence theory for the elliptic case

DOI10.1007/BF00940649zbMath0725.49014MaRDI QIDQ2276750

J. E. Rubio, Wen-bin Liu

Publication date: 1991

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

elliptic variational inequalitiesoptimal shape designmapping methodelectrochemical machiningvariational convergence theory

Mathematics Subject Classification ID

Variational inequalities (49J40) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (9)

On nonlinear parametric variational inequalities ⋮ Shape Optimization for Variational Inequalities of Obstacle Type: Regularized and Unregularized Computational Approaches ⋮ Shape optimization for interface identification with obstacle problems ⋮ Efficient Techniques for Shape Optimization with Variational Inequalities Using Adjoints ⋮ An algorithm based on resolvent operators for solving positively semidefinite variational inequalities ⋮ An algorithm based on resolvent operators for solving variational inequalities in Hilbert spaces ⋮ Optimal shape design for systems governed by variational inequalities. II: Existence theory for the evolution case ⋮ Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities ⋮ Optimal shape design for systems governed by variational inequalities. III: Necessary conditions in the elliptic case

Cites Work

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• On the existence of optimal shapes in contact problems - Perfectly plastic bodies
• Lower-semicontinuity in domain optimization problems
• Shape sensitivity analysis via a penalization method
• On the Definition and Properties of Certain Variational Integrals
• Necessary Conditions for a Domain Optimization Problem in Elliptic Boundary Value Problems
• Electrochemical and Electro-Discharge Machining with a Threshold Current
• On a Variational Inequality Formulation of an Electrochemical Machining Moving Boundary Problem and its Approximation by the Finite Element Method

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