Geodesic
Another Counterexample to Lower Semicontinuity in Calculus of Variations
Journal of convex analysis, Tome 9 (2002) no. 1, pp. 295-3 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 $u \in {\mathbb R}^n$.
Classification : 49J45
Mots-clés : Lower semicontinuity, convex integrals, calculus of variations 
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     author = {R. Cerny and J. Mal\'y},
     title = {Another {Counterexample} to {Lower} {Semicontinuity} in {Calculus} of {Variations}},
     journal = {Journal of convex analysis},
     pages = {295--3},
     year = {2002},
     volume = {9},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2002_9_1_JCA_2002_9_1_a16/}
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R. Cerny; J. Malý. Another Counterexample to Lower Semicontinuity in Calculus of Variations. Journal of convex analysis, Tome 9 (2002) no. 1, pp. 295-3. http://geodesic.mathdoc.fr/item/JCA_2002_9_1_JCA_2002_9_1_a16/