# On the $n$-dimensional Dirichlet problem for isometric maps

created by paolini on 09 Oct 2008
modified on 28 Nov 2016

[BibTeX]

Published Paper

Inserted: 9 oct 2008
Last Updated: 28 nov 2016

Journal: J. Funct. Anal.
Volume: 255
Pages: 3274-3280
Year: 2008
Doi: 10.1016/j.jfa.2008.10.010

Abstract:

We exhibit explicit Lipschitz maps from $\mathbf{R}^{n}$ to $\mathbf{R}^{n}$ which have almost everywhere orthogonal gradient and are equal to zero on the boundary of a cube. We solve the problem by induction on the dimension $n$.

Keywords: isometry, rigid maps