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Scalar Minimizers with Fractal Singular Sets

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Abstract.

Lack of regularity of local minimizers for convex functionals with non-standard growth conditions is considered. It is shown that for every ɛ>0 there exists a function a C α(Ω) such that the functional admits a local minimizer u W 1,p(Ω) whose set of non-Lebesgue points is a closed set Σ with dim ℋ (Σ)>N−p−ɛ, and where 1<p<N<N+α<q<+∞.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213-3890, USA

    Irene Fonseca

  2. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Jan Malý

  3. Department of Mathematics, University of Parma, via M. D’Azeglio 85/a, 43100, Parma, Italy

    Giuseppe Mingione

Authors
  1. Irene Fonseca
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  2. Jan Malý
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  3. Giuseppe Mingione
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Correspondence to Jan Malý.

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V. Šverák

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Fonseca, I., Malý, J. & Mingione, G. Scalar Minimizers with Fractal Singular Sets. Arch. Rational Mech. Anal. 172, 295–307 (2004). https://doi.org/10.1007/s00205-003-0301-6

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  • DOI: https://doi.org/10.1007/s00205-003-0301-6

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