Journal of Optimization Theory and Applications

, Volume 19, Issue 1, pp 3–16

Weak lower semicontinuity of integral functionals

  • C. Olech
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 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 Words

Lower semicontinuityintegral functionalsconvexitymeasurable mapsmeasurable set-valued mapsstrong convergenceweak convergencepointwise convergenceepigraphlower closure

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • C. Olech
    • 1
  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland