INTEGRAL-REPRESENTATION FOR A CLASS OF C1-CONVEX FUNCTIONALS

Authors
DALMASO G DEFRANCESCHI A VITALI E
Citation
G. Dalmaso et al., INTEGRAL-REPRESENTATION FOR A CLASS OF C1-CONVEX FUNCTIONALS, Journal de mathematiques pures et appliquees, 73(1), 1994, pp. 1-46
Citations number
31
Categorie Soggetti
Mathematics, General",Mathematics,Mathematics
Journal title
Journal de mathematiques pures et appliquees → ACNP
ISSN journal
00217824
Volume
73
Issue
1
Year of publication
1994
Pages
1 - 46
Database
ISI
SICI code
0021-7824(1994)73:1<1:IFACOC>2.0.ZU;2-#
Abstract
In view of the applications to the asymptotic analysis of a family of obstacle problems, we consider a class of convex local functionals F(u , A), defined for all functions u in a suitable vector valued Sobolev space and for all open sets A in R(n). Sufficient conditions are given in order to obtain an integral representation of the form F(u, A) = i ntegral-A f(x, u(x))dmu + nu(A), where mu and nu are Borel measures an d f is convex in the second variable.