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Published December 2014 | Submitted
Journal Article Open

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.

Additional Information

© 2014 Springer-Verlag Berlin Heidelberg. Received: 28 August 2013; Revised: 9 April 2014; Published online: 9 May 2014. FIRB2012 'Dinamiche dispersive: analisi di Fourier e metodi variazionali' (J.B., N.V.) and PRIN2009 'Metodi Variazionali e Topologici nello Studio di Fenomeni non Lineari' (J.B.) and U.S. National Science Foundation grants PHY-1068285 and PHY-1347399 (R.F.) are acknowledged. The authors would like to thank E. Lieb and G. Ponce for useful discussions.

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August 20, 2023
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October 18, 2023