On the Brezis-Lieb lemma without pointwise convergence
2015 (English)In: NoDEA. Nonlinear differential equations and applications (Printed ed.), ISSN 1021-9722, E-ISSN 1420-9004, Vol. 22, no 5, 1515-1521 p.Article in journal (Refereed) Published
Brezis-Lieb lemma is an improvement of Fatou Lemma that evaluates the gap between the integral of a functional sequence and the integral of its pointwise limit. The paper proves some analogs of Brezis-Lieb lemma without assumption of convergence almost everywhere. While weak convergence alone brings no conclusive estimates, a lower bound for the gap is found in L (p) , p a parts per thousand yen 3, under condition of weak convergence and weak convergence in terms of the duality mapping. We prove that the restriction on p is necessary and prove few related inequalities in connection to weak convergence.
Place, publisher, year, edition, pages
2015. Vol. 22, no 5, 1515-1521 p.
IdentifiersURN: urn:nbn:se:uu:diva-264830DOI: 10.1007/s00030-015-0333-2ISI: 000361625800022OAI: oai:DiVA.org:uu-264830DiVA: diva2:861855