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.

Bounds for best constants in subcritical Sobolev embeddings

Daniele Cassani;Jianjun Zhang
2019-01-01

Abstract

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.
https://www.journals.elsevier.com/nonlinear-analysis
Sobolev embedding; Trudinger–Moser inequality; Upper and lower estimates;
Cassani, Daniele; Tarsi, Cristina; Zhang, Jianjun
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2079312
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