Abstract

An example is shown of a functional F(u)=∫If(u,u′) dtF(u)=\int_{I}f(u,u')\,dt which is not lower semicontinuous with respect to L1L^1-convergence. The function ff is nonnegative, continuous and strictly convex in the second variable for each u∈Rnu \in {\mathbb R}^n.

Author information

Contact details are reproduced from the original publication and may be historical.

Robert Černý

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

Keywords

  • Lower semicontinuity
  • convex integrals
  • calculus of variations

Mathematics Subject Classification

49J45

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Suggested citation

R. Černý, J. Malý. “Another Counterexample to Lower Semicontinuity in Calculus of Variations.” Journal of Convex Analysis 9 (2002), No. 1, 295–299. https://doi.org/10.68381/jca09017

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press LLC.