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|| u ||∞ ≤ C/√ε || u ||HN/2 + ε for all u ∈ HN/2 + ε(Ω)
is shown for Ω a sufficiently smooth domain in ℝN or a product of N bounded open intervals. This inequality is optimal for any open domain Ω.
Cite this article
Alain Haraux, The best constant for an almost critical Sobolev imbedding. Port. Math. 66 (2009), no. 4, pp. 535–541DOI 10.4171/PM/1854