Hope-lax type formular foru∞t+Hu,Du=0:II

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Abstract
The first order equation u t +H u,D u =0 with u T,x =g x is considered with terminal dat g which is assumed to be only quasiconvex, is a significant generalization of convex functions. The hamiltonian H γ,p is assumed to be homogeneous degree one in p and nondecreasing in γ. It is prove that the explicit solution of such a problem is u t,x = g # γ,p T-t H γ,p # where # refers to the quasiconvex conjugate of the functions in the x variable.

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