Annali di Matematica Pura ed Applicata

, Volume 122, Issue 1, pp 1–60

Some properties of Γ-limits of integral functionals

  • Luciano Carbone
  • Carlo Sbordone

DOI: 10.1007/BF02411687

Cite this article as:
Carbone, L. & Sbordone, C. Annali di Matematica (1979) 122: 1. doi:10.1007/BF02411687


We prove some integral representation theorems for the Γ limit in L1 of sequences of the form\(\int\limits_\Omega {f_h (x,Du)}\) dx in coercivity and bounded growth hypothesis which are optimal as it is checked with examples. These results are utilized to describe the L1 lower semicontinuous envelope of a given functional. We consider also the stability of Γ limits with respect to obstacle type perturbations and prove the homogenization formulas in conditions more generals of those already considered by several authors.

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1979

Authors and Affiliations

  • Luciano Carbone
    • 1
  • Carlo Sbordone
    • 2
  1. 1.Scuola Normale SuperiorePiazza dei CavalieriPisa
  2. 2.Istituto Matematico « R. Caccioppoli »Università di NapoliNapoli