19 feb 2020 -- 11:00 [open in google calendar]
Scuola Normale Superiore, Aula Bianchi Lettere
Due to the wide range of applications in mathematical physics, geometric analysis and string theory, Trudinger-Moser and Adams inequalities have become one of the focus in the field of functional analysis. In this report, I will first recall some classical results about sharp Trudinger-Moser and Admas inequalities on bounded domain and unbounded domain. Then I will introduce my recent work about the existence and uniquness of extremals of sharp Trudinger-Moser and Adams inequalities on the unbounded domain. Finally, I will also present some quantization results for high-order elliptic equations with critical exponential non-linearity.