The prescribed boundary mean curvature problem on the standard \(n\)-dimensional ball

DOI10.1016/j.na.2006.06.030zbMath1190.53033OpenAlexW1984952910MaRDI QIDQ881602

Wael Abdelhedi, Hichem Chtioui

Publication date: 30 May 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.06.030

zbMATH Keywords

variational problemsconformal invariancecritical points at infinitylack of compactnessboundary mean curvature

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (13)

PRESCRIBING MEAN CURVATURE ON 𝔹ⁿ ⋮ Existence results for the fractional Nirenberg problem ⋮ Blowing up solutions for Neumann problem with critical nonlinearity on the boundary ⋮ New existence results for prescribed mean curvature problem on balls under pinching conditions ⋮ Conformal transformation of metrics on the \(n\)-ball ⋮ Compactness and existence results of the prescribing fractional \(Q\)-curvature problem on \(\mathbb{S}^n\) ⋮ On the prescribed fractional \(Q\)-curvatures problem on \(\mathbb{S}^n\) under pinching conditions ⋮ On a Nirenberg-type problem involving the square root of the Laplacian ⋮ Sign-changing bubble for Neumann problem with critical nonlinearity on the boundary ⋮ On a geometric equation involving the Sobolev trace critical exponent ⋮ Prescribed mean curvature equation on the unit ball in the presence of reflection or rotation symmetry ⋮ Conformal metrics with prescribed boundary mean curvature on balls ⋮ A necessary condition for prescribing mean curvature equations in 𝔹ⁿ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The prescribed boundary mean curvature problem on \(\mathbb B^4\)
• Problèmes de Neumann non linéaires sur les variétés riemanniennes
• Sur les transformations conformes des variétés riemanniennes à bord. (On conformal transformations of Riemannian manifolds with boundary)
• Prescribed scalar curvature with minimal boundary mean curvature on \(S^4_+\).
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Periodic solutions of Hamiltonian systems of 3-body type
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• The Yamabe problem on manifolds with boundary
• Algebraic topology methods for the prescribed scalar curvature problem
• A perturbation result for prescribing mean curvature
• A topological hypothesis for the prescribed scalar curvature problem
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• Prescribing scalar and boundary mean curvature on the three dimensional half sphere
• On the Yamabe problem and the scalar curvature problems under boundary conditions
• Conformal metrics with prescribed mean curvature on the boundary
• On the prescribed scalar curvature problem on 4-manifolds
• Conformal metrics on the ball with zero scalar curvature and prescribed mean curvature on the boundary
• Uniqueness theorems through the method of moving spheres
• An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension
• The Nirenberg problem in a domain with boundary
• The Yamabe problem on manifolds with boundary: Existence and compactness results
• On the prescribed scalar curvature problem on the three-dimensional half sphere
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• NIRENBERG'S PROBLEM ON THE 2-DIMENSIONAL HEMI-SPHERE
• The existence of conformal metrics with constant scalar curvature and constant boundary mean curvature

This page was built for publication: The prescribed boundary mean curvature problem on the standard \(n\)-dimensional ball