Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems. (English) Zbl 1320.46026
Summary: In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo-Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb’s Translation Lemma and a Riesz energy version of the Brézis-Lieb lemma.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
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