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Local boundedness of Quasi-minimizers of fully anisotropic scalar variational problems

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Abstract

Some properties of the fully anisotropic Sobolev space \(W^{1,(\Phi _1,\ldots ,\Phi _N)}\) are investigated. In particular extension and embedding theorems for functions in \(W^{1,(\Phi _1,\ldots ,\Phi _N)}\) are deduced. Thanks to a Caccioppoli type inequality it is possible to carry out the De Giorgi procedure to prove the local boundedness of quasi-minimizers of the classical integral functional of the Calculus of Variations satisfying fully anisotropic growth conditions.

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Authors and Affiliations

  1. Istituto Leonardo da Vinci, Via del Terzolle 77, Florence, 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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Correspondence to Tiziano Granucci.

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Granucci, T., Randolfi, M. Local boundedness of Quasi-minimizers of fully anisotropic scalar variational problems. manuscripta math. 160, 99–152 (2019). https://doi.org/10.1007/s00229-018-1055-7

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  • DOI: https://doi.org/10.1007/s00229-018-1055-7

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