We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$|arphi|_L^p(mathbbR^d)le C|arphi|_dot H^s(mathbbR^d)^eta left(iint_mathbbR^d imes mathbbR^d rac|arphi (x)|^q,|arphi (y)|^q|x - y|^d-alpha dx dy ight)^gamma,$$ involving fractional Sobolev norms with $s>0$ and Coulomb type energies with $01$.
Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces / Bellazzini, Jacopo; Ghimenti, Marco; Mercuri, Carlo; Moroz, Vitaly; Van Schaftingen, Jean. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 370:11(2018), pp. 8285-8310.
Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces
Jacopo BellazziniMembro del Collaboration Group
;
2018-01-01
Abstract
We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$|arphi|_L^p(mathbbR^d)le C|arphi|_dot H^s(mathbbR^d)^eta left(iint_mathbbR^d imes mathbbR^d rac|arphi (x)|^q,|arphi (y)|^q|x - y|^d-alpha dx dy ight)^gamma,$$ involving fractional Sobolev norms with $s>0$ and Coulomb type energies with $01$.File in questo prodotto:
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