Blow-up Analysis for a Nonlinear Elliptic Equation with Critical growth and Hardy weight

Abstract: In this talk we will study the asymptotic behaviour of a sequence of solutions to a family of elliptic PDEs with Hardy weight and Sobolev critical growth.  The blow-up analysis will give us conditions under which compactness holds for this sequence and this in turn will help establish the existence of solution(s).The location of the singularity, be it in the interior of the domain or on its boundary, affects the analytical  properties of the equation and makes the two situations quite different. When the singularity is in the interior, then a lower order perturbation suffices for high dimensions, while the geometry of the boundary (curvature) plays a crucial role if the singularity is on the boundary for high dimensions. This is a joint work with Nassif Ghoussoub.