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

Bellazzini, Jacopo and Frank, Rupert L. and Visciglia, Nicola (2014) Maximizers for Gagliardo–Nirenberg inequalities and related non-local problems. Mathematische Annalen, 360 (3-4). pp. 653-673. ISSN 0025-5831.

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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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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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Ministero dell'Istruzione, dell'Università della Ricerca (MIUR)FIRB2012
Ministero dell'Istruzione, dell'Università della Ricerca (MIUR)PRIN2009
Issue or Number:3-4
Record Number:CaltechAUTHORS:20141211-085533969
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52577
Deposited By: Tony Diaz
Deposited On:11 Dec 2014 17:11
Last Modified:03 Oct 2019 07:43

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