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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. https://resolver.caltech.edu/CaltechAUTHORS:20141211-085533969

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00208-014-1046-2 DOIArticle
http://link.springer.com/article/10.1007%2Fs00208-014-1046-2PublisherArticle
http://arxiv.org/abs/1308.5612arXivDiscussion Paper
http://rdcu.be/rF5lPublisherFree ReadCube access
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.
Funders:
Funding AgencyGrant Number
Ministero dell'Istruzione, dell'Università della Ricerca (MIUR)FIRB2012
Ministero dell'Istruzione, dell'Università della Ricerca (MIUR)PRIN2009
NSFPHY-1068285
NSFPHY-1347399
Issue or Number:3-4
Record Number:CaltechAUTHORS:20141211-085533969
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141211-085533969
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52577
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Dec 2014 17:11
Last Modified:03 Oct 2019 07:43

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