How smooth is almost every function in a Sobolev space? (Q879633)
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scientific article; zbMATH DE number 5152586
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | How smooth is almost every function in a Sobolev space? |
scientific article; zbMATH DE number 5152586 |
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How smooth is almost every function in a Sobolev space? (English)
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14 May 2007
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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.
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Sobolev spaces
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Besov spaces
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prevalence
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Haar-null sets
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multifractal functions
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Hölder regularity
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Hausdorff dimension
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wavelet bases
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