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Local Boundedness of Minimizers with Limit Growth Conditions

Author

Listed:
  • Giovanni Cupini

    (Università di Bologna)

  • Paolo Marcellini

    (Università di Firenze)

  • Elvira Mascolo

    (Università di Firenze)

Abstract

The energy integral of the calculus of variations, which we consider in this paper, has a limit behavior when the maximum exponent $$q$$ q , in the growth estimate of the integrand, reaches a threshold. In fact, if $$q$$ q is larger than this threshold, counterexamples to the local boundedness and regularity of minimizers are known. In this paper, we prove the local boundedness of minimizers (and also of quasi-minimizers) under this stated limit condition. Some other general and limit growth conditions are also considered.

Suggested Citation

  • Giovanni Cupini & Paolo Marcellini & Elvira Mascolo, 2015. "Local Boundedness of Minimizers with Limit Growth Conditions," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 1-22, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-015-0722-z
    DOI: 10.1007/s10957-015-0722-z
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    References listed on IDEAS

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    1. Li, S.J. & Li, X.B. & Wang, L.N. & Teo, K.L., 2009. "The Hölder continuity of solutions to generalized vector equilibrium problems," European Journal of Operational Research, Elsevier, vol. 199(2), pages 334-338, December.
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    Cited by:

    1. Mariapia Rosa & Antonio Giuseppe Grimaldi, 2022. "A Local Boundedness Result for a Class of Obstacle Problems with Non-Standard Growth Conditions," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 282-296, October.

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