Geodesic
On symmetry of the extremal in some embedding theorems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 35-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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E. V. Mukoseeva; A. I. Nazarov. On symmetry of the extremal in some embedding theorems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 35-45. http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a2/

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