Maximizers for Gagliardo-Nirenberg inequalities and related non-local problems

preprint2013arXivOpen access

Abstract

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.

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