Journal of Optimization Theory and Applications

, Volume 19, Issue 1, pp 3–16

Weak lower semicontinuity of integral functionals

Authors

  • C. Olech
    • Institute of MathematicsPolish Academy of Sciences
Contributed Papers

DOI: 10.1007/BF00934048

Cite this article as:
Olech, C. J Optim Theory Appl (1976) 19: 3. doi:10.1007/BF00934048

Abstract

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

Copyright information

© Plenum Publishing Corporation 1976