The prescribed boundary mean curvature problem on \(\mathbb B^4\)

DOI10.1016/j.jde.2004.04.016zbMath1108.35070OpenAlexW2037841297MaRDI QIDQ703820

Mohameden Ould Ahmedou, Andrea Malchiodi, Zindine Djadli

Publication date: 11 January 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.04.016

zbMATH Keywords

Blow-up analysisBoundary mean curvatureDegree argumentsSobolev trace critical exponent

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (27)

Concentration solutions to the singularly prescribed Gaussian and geodesic curvatures problem ⋮ PRESCRIBING MEAN CURVATURE ON 𝔹ⁿ ⋮ Conformal metrics on the unit ball with prescribed mean curvature ⋮ Blowing up solutions for supercritical Yamabe problems on manifolds with non-umbilic boundary ⋮ Construction of sign-changing solutions for a harmonic equation with subcritical exponent ⋮ 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 metrics with prescribed scalar and mean curvature ⋮ The Nirenberg problem and its generalizations: a unified approach ⋮ The prescribed boundary mean curvature problem on the standard \(n\)-dimensional ball ⋮ Compactness for a class of Yamabe-type problems on manifolds with boundary ⋮ Construction of blow-up sequences for the prescribed scalar curvature equation on \(S^n\). III: Aggregated and towering blow-ups ⋮ On the prescribed boundary mean curvature problem via local Pohozaev identities ⋮ Prescribing the scalar curvature problem on the four-dimensional half sphere ⋮ On a Nirenberg-type problem involving the half Laplacian: density and multiplicity of solutions ⋮ Existence and multiplicity results for nonlinear critical Neumann problem on compact Riemannian manifolds ⋮ A priori estimates versus arbitrarily large solutions for fractional semi-linear elliptic equations with critical Sobolev exponent ⋮ On the prescribed fractional \(Q\)-curvatures problem on \(\mathbb{S}^n\) under pinching conditions ⋮ Blow-up phenomena for scalar-flat metrics on manifolds with boundary ⋮ Sign-changing bubble for Neumann problem with critical nonlinearity on the boundary ⋮ Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary ⋮ On a min-max procedure for the prescribed boundary mean curvature problem in \(\mathbb{B}_3\) ⋮ On the boundary mean curvature equation on \(\mathbb{B}^{n}\) ⋮ A Morse theoretical approach for the boundary mean curvature problem on \(\mathbb B^4\) ⋮ A compactness theorem for scalar-flat metrics on manifolds with boundary ⋮ Conformal metrics with prescribed boundary mean curvature on balls ⋮ A necessary condition for prescribing mean curvature equations in 𝔹ⁿ

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