Lipschitz continuity of state functions in some optimal shaping

DOI10.1007/s00526-004-0286-5zbMath1062.49035OpenAlexW2092689965MaRDI QIDQ1776567

Michel Pierre, Mohammed Hayouni, Tanguy Briançon

Publication date: 12 May 2005

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-004-0286-5

zbMATH Keywords

regularityoptimal shapeeigenvalue problemLipschitz continuity

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Optimization of shapes other than minimal surfaces (49Q10) Free boundary problems for PDEs (35R35) Variational methods for second-order elliptic equations (35J20)

Related Items (20)

Optimization problems for weighted Sobolev constants ⋮ Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones ⋮ Recent Existence Results for Spectral Problems ⋮ Regularity of minimizers of shape optimization problems involving perimeter ⋮ A free boundary approach to shape optimization problems ⋮ Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold ⋮ On the shape sensitivity of the first Dirichlet eigenvalue for two-phase problems ⋮ Spectral optimization problems ⋮ Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian ⋮ Lipschitz regularity of the eigenfunctions on optimal domains ⋮ Regularity of the optimal shape for the first eigenvalue of the Laplacian with volume and inclusion constraints ⋮ A note on the monotonicity formula of Caffarelli-Jerison-Kenig ⋮ Asymptotic spherical shapes in some spectral optimization problems ⋮ Existence and regularity of minimizers for some spectral functionals with perimeter constraint ⋮ Optimization problems for an energy functional with mass constraint revisited ⋮ 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 ⋮ Lipschitz continuity of the eigenfunctions on optimal sets for functionals with variable coefficients

Cites Work

• Unnamed Item
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• Unnamed Item
• Unnamed Item
• An existence result for a class of shape optimization problems
• A stability result for the magnetic shaping problem
• Some new monotonicity theorems with applications to free boundary problems.
• Spectral synthesis in Sobolev spaces and uniqueness of solutions of the Dirichlet problem
• An Optimization Problem with Volume Constraint
• Un problème inverse en formage des métaux liquides
• Variational problems with two phases and their free boundaries
• Sur la minimisation de la première valeur propre du Laplacien
• Regularity of optimal shapes for the Dirichlet's energy with volume constraint
• On a constrained variational problem with an arbitrary number of free boundaries

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