Видеотека: A. I. Nazarov, On sharp constants in fractional Sobolev and Hardy inequalities

ВИДЕОТЕКА


Международная конференция по функциональным пространствам и теории приближения функций, посвященная 110-летию со дня рождения академика С. М. Никольского 25 мая 2015 г. 14:30, г. Москва, МИАН

On sharp constants in fractional Sobolev and Hardy inequalities A. I. Nazarov^ab ^a Saint Petersburg State University ^b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Аннотация: We discuss the relations between two types of fractional Laplacians – “Dirichlet” and “Navier” ones – in bounded domains in $\mathbb R^n$. Then we prove the coincidence of the Sobolev and Hardy constants relative to these operators of any real order $m\in(0,\frac{n}{2})$. This talk is based on joint papers with Roberta Musina, see [1], [2], [3]. Author was supported by RFBR grant 14-01-00534 and by St.-Petersburg University grant 6.38.670.2013. Язык доклада: английский Список литературы R. Musina, A. I. Nazarov, “On fractional Laplacians”, Comm. in PDEs, 39:9 (2014), 1780–1790 R. Musina, A. I. Nazarov, On fractional Laplacians–2, 2014, arXiv: 1408.3568 R. Musina, A. I. Nazarov, “On the Sobolev and Hardy constants for the fractional Navier Laplacian”, Nonlinear Analysis, 121 (2015), 123–129