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.

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 : 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},
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     number = {3},
     year = {2012},
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     zbl = {1245.28006},
     language = {en},
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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/

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