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A remark on Serrin’s Theorem |
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| Authors: | Nicola Fusco Michele Gori Francesco Maggi |
| Affiliation: | (1) Dipartimento di Matematica e Applicazioni “R.Caccioppoli”, Via Cintia, 80126 Napoli, Italy;(2) Dipartimento di Matematica “L.Tonelli”, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy;(3) Dipartimento di Matematica “U.Dini”, Viale Morgagni 67/A, 50134 Firenze, Italy |
| Abstract: | An approximation theorem for families of weakly coercive convex functions by means of countably many smooth families of convex functions is proved. As a consequence, the classical “three-fold” lower semicontinuity theorem for integral functionals of the Calculus of Variations by James Serrin is unified in one single statement. |
| Keywords: | Primary 49J45 Secondary 52A41 |
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