Worst-case shape optimization for the Dirichlet energy

DOI10.1016/j.na.2016.05.014zbMath1358.49013arXiv1605.05096OpenAlexW2963886964MaRDI QIDQ515919

Bozhidar Velichkov, José Carlos Bellido, Giusseppe Buttazzo

Publication date: 17 March 2017

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.05096

zbMATH Keywords

shape optimizationDirichlet energyworst-case optimization

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Methods involving semicontinuity and convergence; relaxation (49J45) Eigenvalue problems for linear operators (47A75) Variational methods for eigenvalues of operators (49R05)

Related Items (5)

Optimal potentials for problems with changing sign data ⋮ Stochastic Approximation for Optimization in Shape Spaces ⋮ A Shape Optimal Control Problem with Changing Sign Data ⋮ On the Existence of Optimal Potentials on Unbounded Domains ⋮ Risk-averse structural topology optimization under random fields using stochastic expansion methods

Cites Work

• Optimal potentials for Schrödinger operators
• Wiener's criterion and \(\Gamma\)-convergence
• An existence result for a class of shape optimization problems
• Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions
• Variational methods in shape optimization problems
• A linearized approach to worst-case design in parametric and geometric shape optimization
• The method of moving asymptotes—a new method for structural optimization
• Multiple Integrals of Lipschitz Functions in the Calculus of Variations

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