Deville, R.; Matheron, É. Infinite games, Banach space geometry and the eikonal equation. (English) Zbl 1163.91007 Proc. Lond. Math. Soc. (3) 95, No. 1, 49-68 (2007). Summary: We study a class of infinite games which turns out to be closely related to Banach space geometry. Using one of these games, we construct a bounded, differentiable, almost everywhere solution of the eikonal equation \(\| {\nabla} u\| = 1\) on \(\mathbb R^{d}\), with \(d \geqslant 2\). Cited in 2 ReviewsCited in 9 Documents MSC: 91A05 2-person games 46B20 Geometry and structure of normed linear spaces 26B05 Continuity and differentiation questions PDFBibTeX XMLCite \textit{R. Deville} and \textit{É. Matheron}, Proc. Lond. Math. Soc. (3) 95, No. 1, 49--68 (2007; Zbl 1163.91007) Full Text: DOI