Impact of localization of the Hardy potential on the stability of Pohozaev obstructions (joint work with Nassif Ghoussoub (UBC) and Saikat Mazumdar (Bombay)

Speaker: Professor Frédéric Robert, Université de Lorraine
Time: 11-12pm Tuesday 29 November
Location: Carslaw Lecture Theatre 375

Regarding the scalar curvature equation or the Brezis-Nirenberg problem, the classical existence results involve either local terms (in large dimension) or global terms (in low-dimension). Conversely, the Pohozaev obstructions yield nonexistence results. Druet-Laurain proved that these obstructions are stable in low-dimension. 

In this talk, we will discuss the same issue for Hardy-Sobolev equations. It turns out that when the singularity is in the domain, then a similar low-dimensional phenomenon occurs. When the singularity is on the boundary of the domain, we show that there is a universal stability independent of the dimension.