Dimension of images of subspaces under Sobolev mappings

Hencl, Stanislav; Honzík, Petr

doi:10.1016/j.anihpc.2012.01.002

Hencl, Stanislav ; Honzík, Petr

Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 401-411.

Résumé

Let $m < α < p ⩽ n$ and let $f \in W^{1, p} (ℝ^{n}, ℝ^{k})$ be p-quasicontinuous. We find an optimal value of $β (n, m, p, α)$ such that for $ℋ^{β}$ a.e. $y \in {(0, 1)}^{n - m}$ the Hausdorff dimension of $f ({(0, 1)}^{m} \times {y})$ is at most α. We construct an example to show that the value of the optimal β does not increase once p goes below the critical case $p < α$ .

Zbl

DOI : 10.1016/j.anihpc.2012.01.002

Classification : 46E35, 28A78
Mots-clés : Sobolev mapping, Hausdorff dimension

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     author = {Hencl, Stanislav and Honz{\'\i}k, Petr},
     title = {Dimension of images of subspaces under {Sobolev} mappings},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {401--411},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     doi = {10.1016/j.anihpc.2012.01.002},
     zbl = {1245.28006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.002/}
}

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Hencl, Stanislav; Honzík, Petr. Dimension of images of subspaces under Sobolev mappings. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 401-411. doi : 10.1016/j.anihpc.2012.01.002. http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.002/

Bibliographie
Cité par

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