On symmetry of extremals in several embedding theorems

Abstract

We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems $\stackrel{\circ }{W}{}_2^r(-1,1)\hookrightarrow \stackrel{\circ }{W}{}_{\infty }^k(-1,1)$ 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.

9 pages