... e follows: sup|y|≤s u y Su u 1.2 M To obtain the supremum of S i.e., the best constant of Sobolev inequality , we consider the following clamped boundary value problem: −1 M u 2M f x −s < x ... −s, s Clearly, Theorem 1.2 i , ii is rewritten equivalently as follows Corollary 1.3 Let u ∈ H, then the best constant of Sobolev inequality (corresponding to the embedding of H into L∞ −s, s ) ... 2 Boundary Value Problems The fact that ·, · M induces the equivalent norm to the standard norm of the Sobolev Hilbert space of Mth order follows from Poincar´ inequality Let us introduce the...