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; MANFREDI JUAN, J.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 27:5-6(2002), pp. 1139-1159. [10.1081/PDE-120004897]
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.File | Dimensione | Formato | |
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