TY - JOUR
T1 - $\sup  \times \inf$  Inequalities for the Scalar Curvature Equation in Dimensions 4 and 5
AU - Samy Skander Bahoura , 
JO - Analysis in Theory and Applications
VL - 1
SP - 92
EP - 109
PY - 2021
DA - 2021/12
SN - 38
DO - http://doi.org/10.4208/ata.OA-2017-0061
UR - https://global-sci.org/intro/article_detail/ata/20013.html
KW - $\sup \times \inf $, dimension 4 and 5, blow-up, moving-plane method.
AB - <p style="text-align: justify;">We consider the following problem on bounded open set&nbsp; $ \Omega $ of $ {\mathbb R}^n $:</p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20211202/1638432885787647.jpg" title="1638432885787647.jpg" alt="3.JPG"/></p><p style="text-align: justify;">We assume that :</p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20211202/1638432896780682.jpg" title="1638432896780682.jpg" alt="4.JPG"/></p><p style="text-align: justify;">Then, we have a $&nbsp; \sup&nbsp; \times&nbsp; \inf $ inequality for the solutions of the previous equation, namely:</p><p style="text-align: center;"><img src="https://admin.global-sci.org/uploads/ueditor/image/20211202/1638432907866620.jpg" title="1638432907866620.jpg" alt="5.JPG"/></p>