We establish upper and lower estimates for the embedding constants related to the classical Sobolev embeddings H01(Ω)↪Lp(Ω), where Ω⊆RN is a bounded domain or the whole RN and p∈(2,2N∕(N−2)), N≥3. In dimension N=2 we also derive the sharp asymptotic behavior of the embedding constant as p→∞.
Bounds for best constants in subcritical Sobolev embeddings / D. Cassani, C. Tarsi, J. Zhang. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 187(2019 Oct), pp. 438-449. [10.1016/j.na.2019.05.012]
Bounds for best constants in subcritical Sobolev embeddings
C. TarsiSecondo
;
2019
Abstract
We establish upper and lower estimates for the embedding constants related to the classical Sobolev embeddings H01(Ω)↪Lp(Ω), where Ω⊆RN is a bounded domain or the whole RN and p∈(2,2N∕(N−2)), N≥3. In dimension N=2 we also derive the sharp asymptotic behavior of the embedding constant as p→∞.
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