Archive for Rational Mechanics and Analysis

, Volume 166, Issue 4, pp 287–301

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

  • Giuseppe Mingione

DOI: 10.1007/s00205-002-0231-8

Cite this article as:
Mingione, G. Arch. Rational Mech. Anal. (2003) 166: 287. doi:10.1007/s00205-002-0231-8

Abstract

 We estimate the Hausdorff dimension of the singular set of solutions to elliptic systems of the type
$$$$
If the vector fields a and b are Hölder continuous with respect to the variable x with exponent α, then the Hausdorff dimension of the singular set of any weak solution is at most n−2α.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Giuseppe Mingione
    • 1
  1. 1.Dipartimento di Matematica Università di Parma Via M. D'Azeglio 85/a 43100 Parma, Italy e-mail: giuseppe.mingione@unipr.itIT

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