Weak optimal controls in coefficients for linear elliptic problems

DOI10.1007/s13163-010-0030-yzbMath1210.35129arXiv1012.3290OpenAlexW2005926344MaRDI QIDQ2430521

Giusseppe Buttazzo, Peter I. Kogut

Publication date: 6 April 2011

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3290

zbMATH Keywords

weighted Sobolev spacescalculus of variationsdegenerate elliptic equationscontrol in coefficientsLavrentieff phenomenon

Mathematics Subject Classification ID

Perturbations in control/observation systems (93C73) Degenerate elliptic equations (35J70) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20) Weak solutions to PDEs (35D30)

Related Items (18)

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage ⋮ Optimal \(L^2\)-control problem in coefficients for a linear elliptic equation. II. approximation of solutions and optimality conditions ⋮ On optimal controls in coefficients for ill-posed non-linear elliptic Dirichlet boundary value problems ⋮ On approximation of an optimal boundary control problem for linear elliptic equation with unbounded coefficients ⋮ Matrix-valued \(L^1\)-optimal controls in the coefficients of linear elliptic problems ⋮ On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic \(p\)-Laplacian ⋮ Optimal \(L^2\)-control problem in coefficients for a linear elliptic equation. I: Existence result ⋮ On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage ⋮ On optimal control problem for the Perona-Malik equation and its approximation ⋮ Optimality Conditions for $$L^1$$ L 1 -Control in Coefficients of a Degenerate Nonlinear Elliptic Equation ⋮ Optimal control in coefficients for degenerate linear parabolic equations ⋮ Approximation of an optimal control problem in coefficient for variational inequality with anisotropic \(p\)-Laplacian ⋮ On unbounded optimal controls in coefficients for ill-posed elliptic Dirichlet boundary value problems ⋮ On optimal boundary control problem for a strongly degenerate elliptic equation ⋮ Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions ⋮ On an optimal \(L^1\)-control problem in coefficients for linear elliptic variational inequality ⋮ Solvability Issue for Optimal Control Problem in Coefficients for Degenerate Parabolic Variational Inequality ⋮ An Indirect Approach to the Existence of Quasi-optimal Controls in Coefficients for Multi-dimensional Thermistor Problem

Cites Work

• On a variational degenerate elliptic problem
• Anisotropic equations in \(L^ 1\)
• \(L^ \infty\)-solutions for some nonlinear degenerate elliptic and parabolic equations
• Degenerate anisotropic variational inequalities with \(L^1\)-data
• Boundary value problems for some degenerate-elliptic operators
• Weighted Sobolev spaces
• Degenerate equations of monotone type: Lavrent'ev phenomenon and attainability problems
• Characterization of optimal shapes and masses through Monge-Kantorovich equation
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