Dimension of images of subspaces under Sobolev mappings
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 3, p. 401-411

Let m<α<pn and let fW 1,p ( n , k ) be p-quasicontinuous. We find an optimal value of β(n,m,p,α) such that for 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.

DOI : https://doi.org/10.1016/j.anihpc.2012.01.002
Classification:  46E35,  28A78
Keywords: Sobolev mapping, Hausdorff dimension
@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},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     pages = {401-411},
     doi = {10.1016/j.anihpc.2012.01.002},
     zbl = {1245.28006},
     language = {en},
     url = {http://www.numdam.org/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, Volume 29 (2012) no. 3, pp. 401-411. doi : 10.1016/j.anihpc.2012.01.002. http://www.numdam.org/item/AIHPC_2012__29_3_401_0/

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