Abstract
ABSTRACT We consider Hamilton-Jacobi equations in the , where is the Heisenberg group and denotes the horizontal gradient of u. We establish uniqueness of bounded viscosity solutions with continuous initial data . When the hamiltonian H is radial, convex and superlinear the solution is given by the Hopf-Lax formula where the Lagrangian L is the horizontal Legendre transform of H lifted to by requiring it to be radial with respect to the Carnot-Carathéodory metric.
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