Dimension of images of subspaces under Sobolev mappings
Hencl, Stanislav ; Honzík, Petr
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012), p. 401-411 / Harvested from Numdam
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Let m<α<p⩽n and let f∈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∈(0,1) n-m the Hausdorff dimension of f((0,1) m ×{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.

Publié le : 2012-01-01
DOI : https://doi.org/10.1016/j.anihpc.2012.01.002
Classification:  46E35,  28A78 
@article{AIHPC_2012__29_3_401_0,
     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},
     volume = {29},
     year = {2012},
     pages = {401-411},
     doi = {10.1016/j.anihpc.2012.01.002},
     zbl = {1245.28006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2012__29_3_401_0}
}

Hencl, Stanislav; Honzík, Petr. Dimension of images of subspaces under Sobolev mappings. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) pp. 401-411. doi : 10.1016/j.anihpc.2012.01.002. http://gdmltest.u-ga.fr/item/AIHPC_2012__29_3_401_0/

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