# Uniqueness and non degeneracy of positive solutions for critical exponent problem in R^2

### (TIFR CAM, BANGALORE, INDIA)

Date: Jul 01, 2014, time: 09:30

Abstract. Brezis raised the question of uniqueness of positive solutions of critical
exponent problem in a Ball. This problem was settled in dimensions greater than or
equal to three. It was an open problem in two dimensions because of ineffectiveness of
Pohozaev's identity and the critical exponent is of exponential nature. In this talk we will
prove that the solutions are unique and non degenerate in balls of small radius for a
large class of non linearities.