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

VIDEO LIBRARY


International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii May 25, 2015 14:30, Moscow, Steklov Mathematical Institute of RAS

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
Abstract: 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. Language: English References 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