Electron. J. Diff. Equ., Vol. 2015 (2015), No. 164, pp. 1-9.

The infinity(x)-Laplace equation in Riemannian vector fields

Thomas Bieske

We employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of viscosity solutions to the infinity(x)-Laplace equation in Riemannian vector fields. Due to the differences between Euclidean jets and Riemannian jets, the Euclidean method of proof is not valid in this environment.

Submitted June 11, 2015. Published June 17, 2015.
Math Subject Classifications: 35H20, 53C17, 49L25, 31B05, 31C12.
Key Words: Viscosity solution; Riemannian vector field; infinite Laplacian

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Thomas Bieske
Department of Mathematics
University of South Florida
Tampa, FL 33620, USA
email: tbieske@mail.usf.edu

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