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Table 6 Computed values of \(\pmb{C_{p}(\Omega)}\) for a cube domain Ω and \(\pmb{q=2}\) . The numbers of division n are shown in the corresponding parentheses. Theorem 3.1 for \(\pmb{p>3}\) cannot be used when \(\pmb{N=3}\) . Theorem 3.2 can be used for \(\pmb{p=6}\) only when \(\pmb{N=3}\)

From: Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

p Theorem  3.1 Theorem  3.2 Theorem  3.3 [ 19 , Corollary D.1]
3 4.000001 (512) 10.919242 (32,768) 5.947133 (4096) 3.115606 × 104
4 - 16.340789 (4096) 13.241245 (4096) 4.219101 × 104
5 - 18.436348 (4096) 29.676745 (4096) 5.239741 × 104
6 - 20.658471 (1) -