$\sup \times \inf$ Inequalities for the Scalar Curvature Equation in Dimensions 4 and 5

$\sup  \times \inf$  Inequalities for the Scalar Curvature Equation in Dimensions 4 and 5

Year:    2022

Author:    Samy Skander Bahoura

Analysis in Theory and Applications, Vol. 38 (2022), Iss. 1 : pp. 92–109

Abstract

We consider the following problem on bounded open set  $ \Omega $ of $ {\mathbb R}^n $:

3.JPG

We assume that :

4.JPG

Then, we have a $  \sup  \times  \inf $ inequality for the solutions of the previous equation, namely:

5.JPG

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2017-0061

Analysis in Theory and Applications, Vol. 38 (2022), Iss. 1 : pp. 92–109

Published online:    2022-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    $\sup \times \inf $ dimension 4 and 5 blow-up moving-plane method.

Author Details

Samy Skander Bahoura