Asymptotic estimates for Gagliardo-Nirenberg embedding constants (Q1611282)

The authors obtain sharp asymptotic information for the Gagliardo-Nirenberg embedding constants in high dimension. They also show that the Hardy's inequality can be interpreted as the asymptotic limit of the logarithmic Sobolev inequality. The Moser and Nash inequalities illustrate how asymptotic estimates can be obtained for the embedding constants for two sets of Gagliardo-Nirenberg inequalities.