caa a22 4500 606194428 CHVBK 20210128100914.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0333-2 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0333-2 On the Brezis-Lieb lemma without pointwise convergence [Elektronische Daten] [Adimurthi,, Cyril Tintarev] 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 ≥ 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. Springer Basel, 2015 Adimurthi, TIFR CAM, Sharadanagar, P.B. 6503, 560065, Bangalore, India aut Tintarev Cyril Uppsala University, P.O. Box 480, 75 106, Uppsala, Sweden aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1515-1521 1021-9722 22:5<1515 2015 22 30 https://doi.org/10.1007/s00030-015-0333-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0333-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Adimurthi TIFR CAM, Sharadanagar, P.B. 6503, 560065, Bangalore, India aut NATIONALLICENCE 700 1- Tintarev Cyril Uppsala University, P.O. Box 480, 75 106, Uppsala, Sweden aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1515-1521 1021-9722 22:5<1515 2015 22 30