
Journal of Convex Analysis 09 (2002), No. 1, 295300 Copyright Heldermann Verlag 2002 Another Counterexample to Lower Semicontinuity in Calculus of Variations Robert Cerny Dept. Mathematical Analysis, Charles University, Sokolovská 83, 18675 Praha 8, Czech Republic rcerny@karlin.mff.cuni.cz Jan Malý Dept. Mathematical Analysis, Charles University, Sokolovská 83, 18675 Praha 8, Czech Republic maly@karlin.mff.cuni.cz [Abstractpdf] An example is shown of a functional $$ F(u)=\int_{I}f(u,u')\,dt $$ which is not lower semicontinuous with respect to $L^1$convergence. The function $f$ is nonnegative, continuous and strictly convex in the second variable for each $u \in {\mathbb R}^n$. Keywords: Lower semicontinuity, convex integrals, calculus of variations. MSC: 49J45 [ Fulltextpdf (197 KB)] 