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

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.

16 pages

References in corpus (2)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Extremizers for Fourier restriction inequalities: convex arcs