JournalspmVol. 66, No. 4pp. 535–541

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.

Cite this article

Alain Haraux, The best constant for an almost critical Sobolev imbedding. Port. Math. 66 (2009), no. 4, pp. 535–541

DOI 10.4171/PM/1854