On a geometric equation involving the Sobolev trace critical exponent

DOI10.1186/1029-242X-2013-405zbMath1287.35036WikidataQ59299307 ScholiaQ59299307MaRDI QIDQ2441885

Khadijah Sharaf, Hichem Chtioui, Mohamed Ali Al-Ghamdi

Publication date: 28 March 2014

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

variational problemloss of compactness\(\beta\)-flatness conditionboundary mean curvaturecritical point at infinity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational methods for second-order elliptic equations (35J20)

Related Items (2)

Conformal flat metrics with prescribed mean curvature on the boundary ⋮ On the boundary mean curvature equation on \(\mathbb{B}^{n}\)

Cites Work

• On the prescribed Q-curvature problem on \(S^n\)
• Existence results for the prescribed scalar curvature on \(S^3\)
• The scalar-curvature problem on the standard three-dimensional sphere
• Endo-wild representation type and generic representations of finite posets.
• The prescribed boundary mean curvature problem on the standard \(n\)-dimensional ball
• Conformal metrics with prescribed boundary mean curvature on balls
• A perturbation result for prescribing mean curvature
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• 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
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Prescribed scalar curvature on the \(n\)-sphere
• Uniqueness theorems through the method of moving spheres
• An invariant for Yamabe-type flows with applications to scalar-curvature problems in high dimension
• A Morse theoretical approach for the boundary mean curvature problem on \(\mathbb B^4\)
• PRESCRIBING MEAN CURVATURE ON 𝔹ⁿ

This page was built for publication: On a geometric equation involving the Sobolev trace critical exponent