The Singular Set of Minima of Integral Functionals

Abstract

In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals where F is suitably convex with respect to Dv and Hölder continuous with respect to (x,v). In particular, we prove that the Hausdorff dimension of the singular set is always strictly less than n, where .

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Correspondence to Jan Kristensen.

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Communicated by V. Šverák

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Kristensen, J., Mingione, G. The Singular Set of Minima of Integral Functionals. Arch. Rational Mech. Anal. 180, 331–398 (2006). https://doi.org/10.1007/s00205-005-0402-5

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Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Integral Functional