On symmetry of extremals in several embedding theorems

E. V. Mukoseeva; A. I. Nazarov

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arXiv · 1408.3746

On symmetry of extremals in several embedding theorems

E. V. Mukoseeva·A. I. Nazarov

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Abstract

We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems ${\stackrel{\circ}{W}}\vphantom{W}_2^r(-1,1)\hookrightarrow{\stackrel{\circ}{W}}\vphantom{W}_\infty^k(-1,1)$ 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. 2014-08-16. On symmetry of extremals in several embedding theorems. https://arxiv.org/abs/1408.3746

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