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The Singular Set of Lipschitzian Minima of Multiple Integrals

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Abstract

The singular set of any Lipschitzian minimizer of a general quasiconvex functional is uniformly porous and hence its Hausdorff dimension is strictly smaller than the space dimension

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK

    Jan Kristensen

  2. Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53/a, I-43100, Parma, Italy

    Giuseppe Mingione

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  1. Jan Kristensen
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  2. Giuseppe Mingione
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Correspondence to Giuseppe Mingione.

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Communicated by S. Müller.

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Kristensen, J., Mingione, G. The Singular Set of Lipschitzian Minima of Multiple Integrals. Arch Rational Mech Anal 184, 341–369 (2007). https://doi.org/10.1007/s00205-006-0036-2

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  • DOI: https://doi.org/10.1007/s00205-006-0036-2

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