Vol. 301, No. 1, 2019

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Some uniform estimates for scalar curvature type equations

Samy Skander Bahoura

Vol. 301 (2019), No. 1, 55–65
DOI: 10.2140/pjm.2019.301.55
Abstract

We consider the prescribed scalar curvature equation on an open set Ω of n, Δu = V u(n+2)(n2) + un(n2) with V C1,α (0 < α 1), and we prove the inequality supKu × inf Ωu c where K is a compact set of Ω.

In dimension 4, we have an idea on the supremum of the solution of the prescribed scalar curvature if we control the infimum. For this case we suppose the scalar curvature C1,α (0 < α 1).

Keywords
$\sup \times \inf$, nonlinear perturbation, dimension 4, minimal conditions
Mathematical Subject Classification 2010
Primary: 35B44, 35B45, 35B50, 35J60, 53C21
Milestones
Received: 7 November 2017
Revised: 24 October 2018
Accepted: 2 November 2018
Published: 16 September 2019
Authors
Samy Skander Bahoura
Equipe d’Analyse Complexe et Géométrie
Universite Pierre et Marie Curie
Paris
France