Article

Annali di Matematica Pura ed Applicata

, Volume 122, Issue 1, pp 1-60

Some properties of Γ-limits of integral functionals

  • Luciano CarboneAffiliated withScuola Normale Superiore, Piazza dei Cavalieri
  • , Carlo SbordoneAffiliated withIstituto Matematico « R. Caccioppoli », Università di Napoli

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Summary

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.