Published Paper

Inserted: 14 may 2002
Last Updated: 10 jan 2005

Journal: Calc. Var. Partial Differential Equations
Volume: 19
Number: 1
Pages: 23-51
Year: 2004

Abstract:

A chain rule in the space $L^1(div;A)$ is obtained under weak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for functionals of the form $$ int_A ( a( x,u) +b( x,u) \cdot D u) ^+dx,\quad $$ in $W^{1,1}(A)$ with respect to strong convergence in $L^1( A) $ and in turn for general functionals of the form $$ F(u,A):=int_A f(x,u(x),D u(x))\,dx, $$ in $W^{1,1}(A)$. Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.

Keywords: Lower Semicontinuity, Chain Rule

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