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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)

-