E. V. Mukoseeva, A. I. Nazarov, “On symmetry of the extremal in some embedding theorems”, Zap. Nauchn. Sem. POMI, 2014, Volume 425,Pages <nobr>35

This article is cited in 9 papers

On symmetry of the extremal in some embedding theorems

E. V. Mukoseeva^a, A. I. Nazarov^ab

^a St. Petersburg State University, St. Petersburg, Russia
^b St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia

Abstract: We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems $\mathring W_2^r(-1,1)\hookrightarrow\mathring W_\infty^k(-1,1)$ for various $r$ and $k$. The sharp constants for all $r>k$ in the cases $k=4$ and $k=6$ are calculated explicitly as well.

Key words and phrases: sharp constants, embedding theorems, symmetry and asymmetry of extremals.

UDC: 517

Received: 05.08.2014