We exhibit explicit Lipschitz maps from Rn to Rn 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.
On the n-dimensional Dirichlet problem for isometric maps / B. DACOROGNA; P. MARCELLINI; E. PAOLINI. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 255:(2008), pp. 3274-3280. [10.1016/j.jfa.2008.10.010]
On the n-dimensional Dirichlet problem for isometric maps
MARCELLINI, PAOLO;PAOLINI, EMANUELE
2008
Abstract
We exhibit explicit Lipschitz maps from Rn to Rn 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.
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