The infinity Laplacian in infinite dimensions

We study three properties of real-valued functions defined on a Banach space: The absolutely minimizing Lipschitz functions, the viscosity solutions of the infinity Laplacian partial differential equation, and the functions which satisfy comparison with cones. We prove that these notions are equivalent, and we show the existence of such functions. These results are new in the infinite-dimensional case.Received: 14 May 2003, Accepted: 4 August 2003, Published online: 2 April 2004Mathematics Subject Classification (2000): 49L25, 35J60, 54C20