Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Next Article Journal of Convex Analysis 09 (2002), No. 1, 295--300Copyright 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 [Abstract-pdf] 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 [ Fulltext-pdf  (197  KB)]