The Difficulties Semi-Linear in Low dimensions between Brezis and Nirenberg

Abstract

This study discusses existence results for a quasi-linear elliptic equation of critical
Sobolev growth [ ] in the low-dimensional case, where the problem has a global
character which is encoded in sign properties of the “regular” part for the corresponding
Green’s function as in [ ].
Keywords: Brezis- Nirenberg problem, Low dimensions, (1+ -Laplace operator, Blow
up.