Dimension of images of subspaces under Sobolev mappings

  • Stanislav Hencl

    Department of Mathematical Analysis, Charles University, Sokolovská 83, CZ – 186 00 Prague 8, Czech Republic
  • Petr Honzík

    Department of Mathematical Analysis, Charles University, Sokolovská 83, CZ – 186 00 Prague 8, Czech Republic

Abstract

Let and let be -quasicontinuous. We find an optimal value of such that for a.e. the Hausdorff dimension of is at most . We construct an example to show that the value of the optimal does not increase once goes below the critical case .

Cite this article

Stanislav Hencl, Petr Honzík, Dimension of images of subspaces under Sobolev mappings. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 3, pp. 401–411

DOI 10.1016/J.ANIHPC.2012.01.002