How smooth is almost every function in a Sobolev space? | Zendy

Aurélia Fraysse | Zendy; Stéphane Jaffard | Zendy

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How smooth is almost every function in a Sobolev space?

Author(s) -

Aurélia Fraysse,

Stéphane Jaffard

Publication year - 2006

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/469

Subject(s) - multifractal system , sobolev space , hausdorff dimension , mathematics , point (geometry) , fractal , space (punctuation) , function (biology) , dimension (graph theory) , pure mathematics , fractal dimension , hausdorff space , dimension function , besov space , sobolev inequality , mathematical analysis , interpolation space , geometry , computer science , operating system , biochemistry , chemistry , functional analysis , evolutionary biology , gene , biology

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 Holder regularity are fractal sets, and we determine their Hausdor dimension.

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