On symmetry of extremals in several embedding theorems

2014/08/16 by Ekaterina Mukoseeva, E. V. Mukoseeva, Mukoseeva, E. V. +3
Mathematics · #26A06 #49K05 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CA #msc:26A06 #msc:49K05

paper · pdf · doi:10.48550/arxiv.1408.3746

9 pages

arxiv created 2014/08/16 · openalex publication_date 2014/08/16 · arxiv updated 2014/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the symmetry/asymmetry of functions providing sharp constants in the embedding theorems \stackrel∘W\vphantomW₂^r(-1,1)\hookrightarrow\stackrel∘W\vphantomW_∞^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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