Tracking Dirichlet data in \(L^2\) is an ill-posed problem

DOI10.1007/s10957-009-9630-4zbMath1217.49031OpenAlexW2054761368MaRDI QIDQ970580

Karsten Eppler, Helmut Harbrecht

Publication date: 19 May 2010

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

Full work available at URL: https://doi.org/10.1007/s10957-009-9630-4

zbMATH Keywords

free boundary problemboundary element methodill-posednessshape calculusshape Hessian

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Minimal surfaces and optimization (49Q05)

Related Items (9)

Shape optimization approach for solving the Bernoulli problem by tracking the Neumann data: a Lagrangian formulation ⋮ On the new coupled complex boundary method in shape optimization framework for solving stationary free boundary problems ⋮ Numerical solution to a free boundary problem for the Stokes equation using the coupled complex boundary method in shape optimization setting ⋮ Shape optimization and subdivision surface based approach to solving 3D Bernoulli problems ⋮ On a Kohn-Vogelius like formulation of free boundary problems ⋮ On a numerical shape optimization approach for a class of free boundary problems ⋮ An improved shape optimization formulation of the Bernoulli problem by tracking the Neumann data ⋮ A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional ⋮ A physics-informed learning approach to Bernoulli-type free boundary problems

Cites Work

• Shape optimization and fictitious domain approach for solving free boundary problems of Bernoulli type
• An embedding domain approach for a class of 2-d shape optimization problems: Mathematical analysis.
• Efficient treatment of stationary free boundary problems
• Variational approach to shape derivatives for a class of Bernoulli problems
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Analytical and numerical methods in shape optimization
• On the geometric form of Bernoulli configurations
• Differentiation with Respect to the Domain in Boundary Value Problems
• Shape optimization and trial methods for free boundary problems
• Boundary integral representations of second derivatives in shape optimization
• On Convergence in Elliptic Shape Optimization
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