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. 663–682DOI 10.4171/RMI/469