Electron. J. Diff. Equ., Vol. 2016 (2016), No. 125, pp. 1-13.

The infinity(x)-equation in Grushin-type spaces

Thomas Bieske

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

Submitted May 9, 2016. Published May 18, 2016.
Math Subject Classifications: 35H20, 53C17, 49L25, 17B70.
Key Words: Viscosity solutions; Grushin-type spaces; 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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