Delaunay type domains for an overdetermined elliptic problem inn× ℝ and ℍn× ℝ

DOI10.1051/cocv/2014064zbMath1336.58015OpenAlexW2570610560WikidataQ125589935 ScholiaQ125589935MaRDI QIDQ2798001

Filippo Morabito, Pieralberto Sicbaldi

Publication date: 1 April 2016

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

Full work available at URL: https://doi.org/10.1051/cocv/2014064

zbMATH Keywords

bifurcationhomogeneous manifoldsLaplace-Beltrami operatorDelaunay surfacesoverdetermined elliptic problems

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Elliptic equations on manifolds, general theory (58J05) Optimization of shapes other than minimal surfaces (49Q10) Boundary value problems on manifolds (58J32) Overdetermined systems of PDEs with constant coefficients (35N05) Bifurcations in context of PDEs (35B32) PDEs on manifolds (35R01) Bifurcation theory for PDEs on manifolds (58J55)

Related Items (10)

Nontrivial solutions to Serrin's problem in annular domains ⋮ Existence and regularity of Faber-Krahn minimizers in a Riemannian manifold ⋮ Overdetermined elliptic problems in nontrivial contractible domains of the sphere ⋮ Serrin's overdetermined problem on \(\mathbb{S}^N \times\mathbb{R}\) ⋮ On an Electrostatic Problem and a New Class of Exceptional Subdomains of \(\mathbb{R}^3\) ⋮ Linear stability analysis of overdetermined problems with non-constant data ⋮ Serrin's overdetermined problem on the sphere ⋮ Unbounded periodic solutions to Serrin's overdetermined boundary value problem ⋮ Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities ⋮ Overdetermined elliptic problems in onduloid-type domains with general nonlinearities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Bifurcating extremal domains for the first eigenvalue of the Laplacian
• The maximum principle
• Geometrisation of 3-manifolds
• Serrin's result for hyperbolic space and sphere
• New extremal domains for the first eigenvalue of the Laplacian in flat tori
• On an overdetermined elliptic problem
• Geometry and topology of some overdetermined elliptic problems
• Classification of the solutions to an overdetermined elliptic problem in the plane
• A symmetry problem in potential theory
• Stable minimal surfaces in \(M\times \mathbb R\)
• The theory of minimal surfaces in \(M\times \mathbb R\)
• Symmetry and Overdetermined Boundary Value Problems
• Elliptic Partial Differential Equations of Second Order
• Isoperimetric domains in the Riemannian product of a circle with a simply connected space form and applications to free boundary problems

This page was built for publication: Delaunay type domains for an overdetermined elliptic problem inⁿ× ℝ and ℍⁿ× ℝ