A class of Hamilton–Jacobi equations on Banach–Finsler manifolds

The concept of subdifferentiability is studied in the context of C1C1 Finsler manifolds (modeled on a Banach space with a Lipschitz C1C1 bump function). A class of Hamilton–Jacobi equations defined on C1C1 Finsler manifolds is studied and several results related to the existence and uniqueness of viscosity solutions are obtained.