Clustering Phenomena for Linear Perturbation of the Yamabe Equation

DOI10.1017/9781108367639.009zbMath1428.35139arXiv1511.07028OpenAlexW2277390762WikidataQ125699751 ScholiaQ125699751MaRDI QIDQ5234174

Giusi Vaira, Angela Pistoia

Publication date: 25 September 2019

Published in: International Mathematics Research Notices, Partial Differential Equations Arising from Physics and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.07028

zbMATH Keywords

scalar curvatureRicci curvatureLaplace-Beltrami operatorYamabe problemblow-up pointscompact Riemannian manifoldlinear perturbationWeyl curvaturegeometric Paneitz equation

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Elliptic equations on manifolds, general theory (58J05) Higher-order elliptic equations (35J30) Blow-up in context of PDEs (35B44) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (12)

A non-compactness result on the fractional Yamabe problem in large dimensions ⋮ Compactness for a class of Yamabe-type problems on manifolds with boundary ⋮ Clustered solutions to low-order perturbations of fractional Yamabe equations ⋮ Infinite-time blowing-up solutions to small perturbations of the Yamabe flow ⋮ Non-stability of Paneitz-Branson type equations in arbitrary dimensions ⋮ A Paneitz-Branson type equation with Neumann boundary conditions ⋮ Generic properties of critical points of the Weyl tensor ⋮ Positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five ⋮ Towering phenomena for the Yamabe equation on symmetric manifolds ⋮ Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions \(n \geq 7\) ⋮ Non simple blow ups for the Nirenberg problem on half spheres ⋮ Blowing-up solutions to Bopp-Podolsky-Schrödinger-Proca and Schrödinger-Poisson-Proca systems in the electro-magneto-static case

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