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Vector valued minimizers of anisotropic functionals: fractional differentiability and estimate for the singular set

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Abstract

We prove “fractional” higher differentiability for the gradient of minimizers of anisotropic integral functionals, if the growth exponents are no too far apart. This allows us to give an estimate for the Hausdorff dimension of the singular set of the minimizers.

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Authors and Affiliations

  1. Piazza Arechi II, Palazzo De Simone, Università del Sannio, 82100, Benevento, Italy

    Menita Carozza

  2. Dipartimento di Matematica, Università di L’Aquila, Via Vetoio, Coppito, 67010, L’Aquila, Italy

    Francesco Leonetti

  3. Dipartimento di Mat. e Appl. “R. Caccioppoli”, Universitá di Napoli “Federico”, via Cintia, 80126, Napoli, Italy

    Antonia Passarelli di Napoli

Authors
  1. Menita Carozza
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  2. Francesco Leonetti
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  3. Antonia Passarelli di Napoli
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Correspondence to Menita Carozza.

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Carozza, M., Leonetti, F. & Passarelli di Napoli, A. Vector valued minimizers of anisotropic functionals: fractional differentiability and estimate for the singular set. manuscripta math. 128, 51–68 (2009). https://doi.org/10.1007/s00229-008-0224-5

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  • DOI: https://doi.org/10.1007/s00229-008-0224-5

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