On Morrey's inequality in fractional Sobolev spaces.
A talk in the BI.discrete series by
Firoj Sk from Universität Oldenburg
| Abstract: | In the spirit of recent works by Hynd and Seuffert, we study the sharp constant in Morrey's inequality for fractional Sobolev spaces on the entire Euclidean space of dimension $N$, when $0<$$s$$<1$ and $p>1$ are such that $sp>N$. We discuss the existence of the Morrey extremals together with some regularity results. We analyse the sharp asymptotic behaviour of the Morrey constant in the following cases: i) when $N, p$ are fixed with $N$$<$$p,$ and $s$ go to $N/p,$ ii) when $s, N$ are fixed, and $p$ tends to infinity, iii) when $N, p$ are fixed with $N$$<$$p,$ and $s$ goes to $1$. We further demonstrate the convergence of extremals as $s$ goes to $1$, which ensures the consistency of the well-known local results by Hynd and Seuffert. This talk is based on joint works with L. Brasco and F. Prinari. Within the CRC this talk is associated to the project(s): A7 |