Bounds for best constants in subcritical Sobolev embeddings. (October 2019)

• Record Type: Journal Article
• Authors: Cassani, Daniele; Tarsi, Cristina; Zhang, Jianjun
• Is Part Of: Nonlinear analysis. Volume 187(2019)
• Page Start: 438
• Page End: 449
• Publication Date: 2019-10
• Subjects: 35B25 -- 35B33 -- 35J61; Sobolev embedding -- Trudinger–Moser inequality -- Upper and lower estimates; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.05.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish upper and lower estimates for the embedding constants related to the classical Sobolev embeddings H 0 1 ( Ω ) ↪ L p ( Ω ), where Ω ⊆ R N is a bounded domain or the whole R N and p ∈ ( 2, 2 N ∕ ( N − 2 ) ), N ≥ 3 . In dimension N = 2 we also derive the sharp asymptotic behavior of the embedding constant as p → ∞ .