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MR2241425 42B25 (26D15 35J20 46E35)
Demʹyanov, A. V.; Nazarov, A. I. On the existence of an extremal function in Sobolev embedding theorems with a limit exponent. (Russian) Algebra i Analiz 17 (2005), no. 5, 105--140; translation in St. Petersburg Math. J. 17 (2006), no. 5, 773–796
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