Carnegie Mellon
Department of Mathematical 

Giovanni Leon, Dipartimento di Scienze e Tecnologia Avanzate, Universita del Piemonte Orientale.

"A chain rule in $L^1(div;\Omega)$ and its applications to lower semicontinuity"


A chain rule in the space $L^1(div;\Omega)$ is obtained underweak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for functionals of the form

\begin{displaymath}\int_\Omega (a(x,u) +b(x,u) \cdot \nabla u)^+ dx,\quad u\in

with respect to strong convergence in $L^1(\Omega)$, and in turn for general functionals of the form

\begin{displaymath}F(u,\Omega ):=\int_\Omega f(x,u(x),\nabla u(x))\,dx,\quad u\in
W^{1,1}(\Omega ).\end{displaymath}

Classical results of Serrin, and De Giorgi, Buttazzo and Dal Maso are extended and generalized.

TUESDAY, April 16, 2002
Time: 1:30 P.M.
Location: Physical Plant Building 300