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A Relaxation Result in the Vectorial Setting and Power Law Approximation for Supremal Functionals

Author

Listed:
  • Francesca Prinari

    (Università di Ferrara)

  • Elvira Zappale

    (Università degli Studi di Salerno)

Abstract

We provide relaxation for not lower semicontinuous supremal functionals defined on vectorial Lipschitz functions, where the Borel level convex density depends only on the gradient. The connection with indicator functionals is also enlightened, thus extending previous lower semicontinuity results in that framework. Finally, we discuss the power law approximation of supremal functionals, with nonnegative, coercive densities having explicit dependence also on the spatial variable, and satisfying minimal measurability assumptions.

Suggested Citation

  • Francesca Prinari & Elvira Zappale, 2020. "A Relaxation Result in the Vectorial Setting and Power Law Approximation for Supremal Functionals," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 412-452, August.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:2:d:10.1007_s10957-020-01712-y
    DOI: 10.1007/s10957-020-01712-y
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