How smooth is almost every function in a Sobolev space?
Rev. Mat. Iberoamericana, Tome 22 (2006) no. 2, p. 663-682 / Harvested from Project Euclid
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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.
Publié le : 2006-09-14
Classification:  Sobolev spaces,  Besov spaces,  prevalence,  Haar-null sets,  multifractal functions,  Hölder regularity,  Hausdorff dimension,  wavelet bases,  28C20,  26A15,  26A21,  46E35,  28A80,  42C40,  54E52 
@article{1161871351,
     author = {Fraysse
,  
Aur\'elia and Jaffard
,  
St\'ephane},
     title = {How smooth is almost every function in a Sobolev space?},
     journal = {Rev. Mat. Iberoamericana},
     volume = {22},
     number = {2},
     year = {2006},
     pages = { 663-682},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1161871351}
}

Fraysse
,  
Aurélia; Jaffard
,  
Stéphane. How smooth is almost every function in a Sobolev space?. Rev. Mat. Iberoamericana, Tome 22 (2006) no. 2, pp.  663-682. http://gdmltest.u-ga.fr/item/1161871351/