Journal of Convex Analysis 09 (2002), No. 1, 295--300
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
[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
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