Maria J. Esteban is a specialist of nonlinear partial differential equations and mathematical physics who works at the University Paris-Dauphine. She is director of research at CNRS.

She has been president of SMAI, the French Applied Mathematics Society, and will be the next president of ICIAM, the International Council for Industrial and Applied Mathematics.

She is member of Jakiunde, the Basque Academy of Sciences, Arts and Letters, knight of the National Order of Merit (France), honorary fellow of RSME (Royal Spanish Mathematical Society), and the Eisele Stiftung Fellow for the year 2013-2014.

She was plenary speaker at the International Congress of Mathematics Physics (Lisbon, 2003), keynote speaker at the opening of the Mathematical Year 2014, organized by the South Korean Parliament, and Invited speaker at the European Congress of Mathematics, Amsterdam, 2008 Moreover, she gave the Ladyzhenskaya Lecture at University of Leipzig in 2008, and the Mary Cartwright Lecture (LMS) in 2015.

In this talk I will present recent results, obtained in collaboration with J. Dolbeault and M. Loss, proving the radial symmetry of the optimizers of Caffarelli-Kohn-Nirenberg inequalities whenever they are local minima in the full functional space. These results are optimal and close a series of works proving partial results. The method used to obtain this result, which actually proves the uniqueness of positive solutions for the corresponding Euler-Lagrange equations, is based on a nonlinear fast diffusion flow which is applied around any positive solution to explore the energy landscape around it.

Written by: Zhang Jiang

Source: PKU Lecture Hall