The best constant for an almost critical Sobolev imbedding

Alain Haraux

doi:10.4171/pm/1854

JournalspmVol. 66, No. 4pp. 535–541

The best constant for an almost critical Sobolev imbedding

Alain Haraux
Université Pierre et Marie Curie, Paris, France

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Abstract

The inequality

∥ u ∥_{\infty} \leq \frac{C}{\sqrt ε} ∥ u ∥_{H^{N /2 + ε}} for all u \in H^{N /2 + ε} (Ω),

is shown for $Ω$ a sufficiently smooth domain in $R^{N}$ 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