We consider Hamilton-Jacobi equations in the Heisenberg group . 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 the algebra by requiring it to be radial with respect to the Carnot-Carathéodory metric.

A VERSION OF THE {H}OPF-{L}AX FORMULA IN THE {H} EISENBERGGROUP

STROFFOLINI, BIANCA;
2002

Abstract

We consider Hamilton-Jacobi equations in the Heisenberg group . 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 the algebra by requiring it to be radial with respect to the Carnot-Carathéodory metric.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/1345
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