Bounds for best constants in subcritical Sobolev embeddings

We establish upper and lower estimates for the embedding constants related to the classical Sobolev embeddings H-0(1)(Omega) hooked right arrow L-p (Omega), where Omega subset of R-N is a bounded domain or the whole R-N and p is an element of(2, 2N/(N - 2)), N >= 3. In dimension N = 2 we also derive the sharp asymptotic behavior of the embedding constant as p -> infinity. (C) 2019 Elsevier Ltd. All rights reserved.