APS
Speaker: Amal Das, IIT Bombay
Host: Saikat Mazumdar
Title: Hardy-Sobolev inequality with full boundary singularity and obtainability of its sharp constant
Time, day and date: 2:15:00 PM – 3:15:00 PM, Friday, September 26
Venue: Ramanujan Hall
Abstract: We will study the Hardy-Sobolev inequality with full boundary singularity and also show that the best constant is achieved by some nonzero function under some (local) geometric conditions on the boundary of the domain. This is equivalent to a variational problem, and a solution can be obtained as an extremal for this variational problem. The core issue is to show the convergence of minimizing sequence, which we will see holds, provided one is strictly below a threshold energy level given by the best Hardy-Sobolev constant in $\mathbb{R}^n_ +$.