Contributed Papers

Journal of Optimization Theory and Applications

, Volume 19, Issue 1, pp 3-16

First online:

Weak lower semicontinuity of integral functionals

  • C. OlechAffiliated withInstitute of Mathematics, Polish Academy of Sciences

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A lower semicontinuity theorem for integral functionals is proved underL 1-strong convergence of the trajectories andL 1-weak convergence of the control functions. An alternative statement is also proved under pointwise convergence of the trajectories.

Key Words

Lower semicontinuity integral functionals convexity measurable maps measurable set-valued maps strong convergence weak convergence pointwise convergence epigraph lower closure