Sharp Gagliardo-Nirenberg inequalities and mass transport theory. (English) Zbl 1155.35320
In the paper, the link between Gagliardo-Nirenberg inequalities and Mmass transport theory is discussed. Sharp constants and optimal functions of the Gagliardo-Nirenberg inequalities are obtained explicitly in dimension \(n=1\) by using solutions of a certain ordinary differential equation.
Reviewer: Jiří Šremr (Brno)
MSC:
| 35J20 | Variational methods for second-order elliptic equations |
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
Keywords:
Gagliardo-Nirenberg inequalities; best constants; optimal functions; mass transport theory; displacement convexityReferences:
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