BooksStandalone TitlesCollected Volumepp. 1–43

Scalar minimizers with maximal singular sets and lack of Meyers property

  • Anna Balci

    Charles University, Prague, Czech Republic; Bielefeld University, Germany
    ORCID

  • Lars Diening

    Bielefeld University, Germany
    ORCID

  • Mikhail Surnachev

    Keldysh Institute of Applied Mathematics, Moscow, Russia
    ORCID
Scalar minimizers with maximal singular sets and lack of Meyers property cover
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Abstract

We present a general procedure to construct examples of convex scalar variational problems which admit minimizers with large singular sets. The dimension of the set of singularities is maximal and the minimizer has no higher integrability property (failure of Meyers property).