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Infinite games, Banach space geometry and the Eikonal equation
Author(s) -
Deville R.,
Matheron É.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm005
Subject(s) - mathematics , eikonal equation , banach space , differentiable function , bounded function , class (philosophy) , mathematical analysis , space (punctuation) , geometry , pure mathematics , linguistics , philosophy , artificial intelligence , computer science
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 ‖ ∇ u ‖ = 1 on ℝ d , with d ⩾ 2.
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