JournalspmVol. 66 / No. 4DOI 10.4171/pm/1854

The best constant for an almost critical Sobolev imbedding

  • Alain Haraux

    Université Pierre et Marie Curie, Paris, France
The best constant for an almost critical Sobolev imbedding cover

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Abstract

The inequality

|| 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.