Q1406936
type: Item
instance of: scholarly article
title: Différentes estimations de \(\sup u\times \inf u\) pour l'équation de la courbure scalaire prescrite en dimension \(n\geqslant 3\). (Various estimates of \(\sup u\times \inf u\) for the equation of prescribed scalar curvature in dimension \(n\geqslant 3\))
zbMATH Open document ID: 1035.53049
DOI: 10.1016/S0021-7824(02)00003-X
author: Samy Skander Bahoura
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2003-09-07T00:00:00Z
review text: The main result of the paper shows that positive solution \(u\) of the equation of prescribed scalar curvature, on a compact set in a Riemannian manifold \((M,g)\), is uniformly bounded. Then, on a compact Riemannian manifold the inequalities \(\sup_M u\times\inf_M u\geq c> 0\) if \(n\geq 3\), \(\sup_M u+\inf_M u\geq c\) if \(n= 2\) are valid.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1975975
zbMATH Keywords: prescribed scalar curvature
zbMATH Keywords: Yamabe problem
zbMATH Keywords: Harnack inequality
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
cites work: Q4398855
cites work: Q4288397
cites work: A sup+inf inequality for some nonlinear elliptic equations involving exponential nonlinearities
cites work: Blowing up with infinite energy of conformal metrics on Sn
cites work: Global and local behavior of positive solutions of nonlinear elliptic equations
cites work: Harnack type inequality: The method of moving planes
cites work: Q4052566
cites work: Q3961209
cites work: On the existence of solutions of nonlinear elliptic boundary value problems
label: Différentes estimations de \(\sup u\times \inf u\) pour l'équation de la courbure scalaire prescrite en dimension \(n\geqslant 3\). (Various estimates of \(\sup u\times \inf u\) for the equation of prescribed scalar curvature in dimension \(n\geqslant 3\))
description: scientific article; zbMATH DE number 1975975