ERC Workshop on Existence and Regularity for Nonlinear Systems of Partial Differential Equations*

Uniqueness and non degeneracy of positive solutions for critical exponent problem in R²

speaker: Adi Adimurthi (TIFR CAM, BANGALORE, INDIA)

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.

timetable:
Tue 1 Jul, 9:30 - 10:20, Aula Dini
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