Email this article On the traces of Sobolev functions on Lipschitz surfaces
- Authors: Romanov A.S.1
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch
- Issue: Vol 95, No 3 (2017)
- Pages: 243-246
- Section: Mathematics
- URL: https://journal-vniispk.ru/1064-5624/article/view/225069
- DOI: https://doi.org/10.1134/S1064562417030127
- ID: 225069
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Abstract
Functions from the Sobolev spaces Wp1(Q) are considered on a unit cube Q ⊂ Rn, and the properties of their traces on Lipschitz surfaces are examined. The relation is found between the Hölder exponent α and the Hausdorff dimension of the family of poor k-dimensional planes Γ on which the traces do not belong to Cα(Γ). For the corresponding families of poor k-dimensional Lipschitz surfaces, estimates in terms of p-modules are obtained.
About the authors
A. S. Romanov
Sobolev Institute of Mathematics, Siberian Branch
Author for correspondence.
Email: asrom@math.nsc.ru
Russian Federation, Novosibirsk, 630090
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