Regularity of optimal shapes for the Dirichlet's energy with volume constraint

DOI10.1051/cocv:2003038zbMath1118.35078OpenAlexW1989403844MaRDI QIDQ5465542

Tanguy Briançon

Publication date: 9 August 2005

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2004__10_1_99_0

zbMATH Keywords

calculus of variationsfree boundaryShape optimizationgeometrical measure theory

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Optimization of shapes other than minimal surfaces (49Q10) Free boundary problems for PDEs (35R35) Variational methods for second-order elliptic equations (35J20)

Related Items (11)

Regularity of minimizers of shape optimization problems involving perimeter ⋮ Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold ⋮ An Escape Time Formulation for Subgraph Detection and Partitioning of Directed Graphs ⋮ Spectral optimization problems ⋮ Regularity of the optimal shape for the first eigenvalue of the Laplacian with volume and inclusion constraints ⋮ Lipschitz continuity of state functions in some optimal shaping ⋮ Counterexamples to symmetry for partially overdetermined elliptic problems ⋮ Optimal shapes for general integral functionals ⋮ Regularity of optimal ship forms based on Michell's wave resistance ⋮ Existence and regularity of optimal shapes for elliptic operators with drift ⋮ Faber-Krahn inequalities in sharp quantitative form

Cites Work

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• Plane harmonic measures live on sets of \(\sigma\)-finite length
• An Optimization Problem with Volume Constraint
• Variational problems with two phases and their free boundaries

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