Dimension of images of subspaces under Sobolev mappings

0380503 - MÚ 2013 RIV FR eng J - Journal Article
Hencl, S. - Honzík, Petr
Dimension of images of subspaces under Sobolev mappings.
Annales de l'Institut Henri Poincaré. Analyse non Linéaire. Roč. 29, č. 3 (2012), s. 401-411. ISSN 0294-1449. E-ISSN 1873-1430
R&D Projects: GA AV ČR KJB100190901
Institutional research plan: CEZ:AV0Z10190503
Keywords : Sobolev mapping * Hausdorff dimension
Subject RIV: BA - General Mathematics
Impact factor: 1.550, year: 2012
http://www.sciencedirect.com/science/article/pii/S0294144912000108

Let In < alpha < p <= n and let f is an element of W-1.P(R-n, R-k) be p-quasicontinuous. We find an optimal value of beta(n, m, p, alpha) such that for H-beta a.e. y is an element of (0. 1)(n-m) the Hausdorff dimension of f((0, 1)(m) x {y}) is at most alpha. We construct an example to show that the value of the optimal 11 does not increase once p goes below the critical case p < alpha.
Permanent Link: http://hdl.handle.net/11104/0211195