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Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces / Jacopo Bellazzini; Marco Ghimenti; Carlo Mercuri; Vitaly Moroz; Jean Van Schaftingen

Transactions of the American Mathematical Society, Start page: 1

Swansea University Author: Mercuri, Carlo

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DOI (Published version): 10.1090/tran/7426

Abstract

We prove a family of interpolation inequalities which hold in the context of "Coulomb-Sobolev" spaces associated with the fractional Laplacian operator. More specifically we generalise a notion of Coulomb-Sobolev space which have been introduced in a former paper of Mercuri-Moroz-Van Schaf...

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Published in: Transactions of the American Mathematical Society
ISSN: 0002-9947 1088-6850
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa35990
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Abstract: We prove a family of interpolation inequalities which hold in the context of "Coulomb-Sobolev" spaces associated with the fractional Laplacian operator. More specifically we generalise a notion of Coulomb-Sobolev space which have been introduced in a former paper of Mercuri-Moroz-Van Schaftingen, and prove in this setting a family of embedding theorems into L^p spaces, dealing with both the radially symmetric and the non-radial cases. This study is relevant when dealing with models where the fractional Laplacian operator is involved, together with an interaction term (which has the form of a double integral, containing a Coulomb or more in general a Riesz type kernel). Some models on graphene are strongly related to the mathematical tools which we studied in this paper.
Item Description: Published in Transactions of the American Mathematical Society 2018. Copyright 2018 American Mathematical Society.
College: College of Science
Start Page: 1