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Regularity for local minima of a special class of vectorial problems with fully anisotropic growth

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Abstract

In this paper we establish boundedness and continuity results for vectorial local minimizers of special classes of integral functionals. In particular we consider a class of vectorial problems in which the energy density satisfies fully anisotropic growth. We analyze two different types of anisotropic growths connected with the Orlicz Sobolev spaces. We prove boundedness results for energy densities satisfying anisotropic growth, moreover for particular energy densities we get Hölder continuity results by proving that each component belongs to a suitable De Giorgi class. Finally, we provide specific non-trivial instances of our results.

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Acknowledgements

We should like to thank the anonymous referees for their useful suggestions.

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  1. Istituto Leonardo da Vinci, Via del Terzolle 91, Firenze, Italy

    Tiziano Granucci

  2. Bologna, Italy

    Monia Randolfi

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  1. Tiziano Granucci
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  2. Monia Randolfi
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Granucci, T., Randolfi, M. Regularity for local minima of a special class of vectorial problems with fully anisotropic growth. manuscripta math. 170, 677–772 (2023). https://doi.org/10.1007/s00229-021-01360-0

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