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Table 4 Computed values of \(\pmb{C_{p}(\Omega)}\) for a regular triangle domain Ω and \(\pmb{q=2}\) . The numbers of division n are shown in the corresponding parentheses. Theorem 3.1 cannot be used for \(\pmb{p>4}\) when \(\pmb{N=2}\)

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 2.580982 (16) 4.097053 (256) 2.366856 (4) 2.538335 × 104
4 2.465500 (4) 5.700515 (64) 2.709475 (4) 3.553398 × 104
5 - 6.330220 (64) 3.042818 (4) 4.464990 × 104
6 - 7.477243 (64) 3.353176 (4) 5.297547 × 104
7 - 7.601403 (16) 3.641844 (4) 6.067602 × 104
8 - 7.750471 (16) 3.911816 (4) 6.786738 × 104
9 - 7.933346 (16) 4.165864 (4) 7.463399 × 104
10 - 8.133664 (16) 4.406282 (4) 8.103954 × 104
20 - 10.219436 (16) 6.341217 (4) 1.326097 × 105
30 - 12.055827 (16) 7.622031 (16) 1.717928 × 105
40 - 13.666509 (16) 8.748299 (16) 2.045371 × 105
50 - 15.112804 (16) 9.869218 (16) 2.331904 × 105
60 - 16.059718 (64) 10.876336 (16) 2.589578 × 105
70 - 17.313793 (64) 11.798394 (16) 2.825529 × 105
80 - 18.483221 (64) 12.653794 (16) 3.044383 × 105