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.
A remark on Serrin's theorem / N. FUSCO; M. GORI; F. MAGGI. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 13:(2006), pp. 425-433. [10.1007/s00030-006-4018-8]
A remark on Serrin's theorem
GORI, MICHELE;MAGGI, FRANCESCO
2006
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.
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