Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with umbilic boundary

DOI10.1016/j.na.2022.113206OpenAlexW4313252346MaRDI QIDQ2688999

Marco Ghimenti, Anna Maria Micheletti

Publication date: 6 March 2023

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

Full work available at URL: https://arxiv.org/abs/2204.06037

zbMATH Keywords

compactnessYamabe problemblow up analysisumbilic boundary

Mathematics Subject Classification ID

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

Cites Work

• Unnamed Item
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• A compactness theorem for scalar-flat metrics on manifolds with boundary
• An existence theorem of conformal scalar-flat metrics on manifolds with boundary
• The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds
• Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
• Blow-up phenomena for linearly perturbed Yamabe problem on manifolds with umbilic boundary
• Prescribed scalar curvature on the \(n\)-sphere
• The Yamabe problem on manifolds with boundary: Existence and compactness results
• A compactness result for scalar-flat metrics on low dimensional manifolds with umbilic boundary
• Compactness results for linearly perturbed Yamabe problem on manifolds with boundary
• Blowing-up solutions for supercritical Yamabe problems on manifolds with umbilic boundary
• Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary
• Compactness for conformal scalar-flat metrics on umbilic boundary manifolds
• Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary
• The effect of linear perturbations on the Yamabe problem
• Sharp asymptotics and compactness for local low energy solutions of critical elliptic systems in potential form
• A priori estimates for the Yamabe problem in the non-locally conformally flat case
• Existence results for the Yamabe problem on manifolds with boundary
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• A 𝐶⁰-theory for the blow-up of second order elliptic equations of critical Sobolev growth