How smooth is almost every function in a Sobolev space?
type: Item
instance of: scholarly article
title: How smooth is almost every function in a Sobolev space?
zbMATH Open document ID: 1155.28302
DOI: 10.4171/RMI/469
author: Aurélia Fraysse
author: Stéphane Jaffard
published in: Revista Matemática Iberoamericana
publication date: 2007-05-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1161871351
full work available at URL: https://eudml.org/doc/41987
review text: Summary: 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.
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5152586
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Besov spaces
zbMATH Keywords: prevalence
zbMATH Keywords: Haar-null sets
zbMATH Keywords: multifractal functions
zbMATH Keywords: Hölder regularity
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: wavelet bases
MaRDI profile type: Publication
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OpenAlex ID: W1998045092
description: scientific article; zbMATH DE number 5152586