14 mar 2019 -- 15:00   [open in google calendar]

Scuola Normale Superiore, Aula Dini (Castelletto)

Abstract.

I will explain why certain Riesz potentials and their sharp estimates are relevant in several different contexts including $L$-problem of moments (A.A. Markov, M. Krein, N. Akhiezer, M. Putinar), exponential transform of quadrature domains and domain identification (M. Putinar, B. Gustafsson, G. Golub, P. Milanfar), an exponential transform and regularity of free boundaries in two dimensions (M. Putinar, B. Gustafsson), gradient potential estimates (Adams, Hedberg, Mingione) and also very recent appears in monotonicity formulae (J. Zhu, 2018). I will also give an overview of my recent results in this direction. The emphasis will be given on the applications to the $L$-moment problem and exponential transforms