Weak lower semicontinuity of integral functionals
A lower semicontinuity theorem for integral functionals is proved underL1-strong convergence of the trajectories andL1-weak convergence of the control functions. An alternative statement is also proved under pointwise convergence of the trajectories.
Key WordsLower semicontinuity integral functionals convexity measurable maps measurable set-valued maps strong convergence weak convergence pointwise convergence epigraph lower closure
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