Bounds for best constants in subcritical Sobolev embeddings. (October 2019) - Cassani, Daniele; Tarsi, Cristina; Zhang, Jianjun
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 → ∞ .