Counterexamples to symmetry for partially overdetermined elliptic problems

DOI10.1524/anly.2009.1016zbMath1180.35200arXiv0902.2947OpenAlexW1978102617WikidataQ124857454 ScholiaQ124857454MaRDI QIDQ3636181

Jimmy Lamboley, Gazzola, Filippo, Michel Pierre, Ilaria Fragalà

Publication date: 30 June 2009

Published in: Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.2947

zbMATH Keywords

shape optimizationoverdetermined boundary value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Optimization of shapes other than minimal surfaces (49Q10) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (9)

On symmetry of nonnegative solutions of elliptic equations ⋮ A new symmetry criterion based on the distance function and applications to PDE's ⋮ Symmetry results for overdetermined problems on convex domains via Brunn-Minkowski inequalities ⋮ On the stability of \(k\)-Hessian overdetermined and partially overdetermined problems in planar domain ⋮ A Serrin-type problem with partial knowledge of the domain ⋮ A local symmetry result for linear elliptic problems with solutions changing sign ⋮ An overdetermined problem associated to the Finsler Laplacian ⋮ About Hölder-regularity of the convex shape minimizing λ₂ ⋮ Symmetry of Nonnegative Solutions of Elliptic Equations via a Result of Serrin

Cites Work

• Partially overdetermined elliptic boundary value problems
• An existence result for a class of shape optimization problems
• Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions
• Lipschitz continuity of state functions in some optimal shaping
• Steiner symmetric extremals in Pólya-Szegő-type inequalities
• A symmetry problem in potential theory
• Partial regularity for weak solutions of an elliptic free boundary problem
• Regularity of optimal shapes for the Dirichlet's energy with volume constraint

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