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Infinite games, Banach space geometry and the eikonal equation. (English) Zbl 1163.91007
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 $$d \geqslant 2$$.

##### MSC:
 91A05 2-person games 46B20 Geometry and structure of normed linear spaces 26B05 Continuity and differentiation questions
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