Subelliptic Hamilton-Jacobi equations: the coercive evolution case

Abstract

We prove the existence and uniqueness of a viscosity (Lipschitz) solution relative to bounded uniformly continuous (Lipschitz) initial data for a subelliptic evolution Hamilton–Jacobi equation with a coercive Hamiltonian. Moreover we also prove a comparison property for viscosity sub- and supersolutions.

Keywords:

• partial differential equations in Carnot groups
• viscosity solutions of Hamilton–Jacobi equations
• regularity

AMS Subject Classifications::

• 35H20
• 49L25
• 35B65