A class of Hamilton-Jacobi equations on Banach-Finsler manifolds
  The concept of subdifferentiability is studied in the context of $C^1$ Finsler manifolds (modeled on a Banach space with a Lipschitz $C^1$ bump function). A class of Hamilton-Jacobi equations defined on $C^1$ Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained. 
J.A. Jaramillo, M. Jimenez-Sevilla, J.L. Rodenas-Pedregosa and L.   Sanchez-Gonzalez
math.FA math.AP math.DG