JournalsrmiVol. 22, No. 2pp. 663–682

How smooth is almost every function in a Sobolev space?

  • Aurélia Fraysse

    Université Paris Est, Créteil, France
  • Stéphane Jaffard

    Université Paris Est, Créteil, France
How smooth is almost every function in a Sobolev space? cover
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Abstract

We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.

Cite this article

Aurélia Fraysse, Stéphane Jaffard, How smooth is almost every function in a Sobolev space?. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 663–682

DOI 10.4171/RMI/469