Speaker: Amal Das
Time: 26 September, 4-5 pm
Venue: Ramanujan Hall.
Title: Concentration phenomena for a Sobolev critical equation.
Abstract: In this report we will study a non-linear elliptic equation on a
bounded smooth domain in R^n with critical Sobolev exponent, the so called
Brezis-Nirenberg problem. The equation can be written in a variational
form and weak solutions can be obtained as the critical points, in
particular, minimizers of the corresponding energy functional. The core
issue is to show that there is no concentration and minimizing sequence
converges, which holds provided one is strictly below a threshold energy
level given by the best Sobolev constant in R^n.