Abstract
The method of moving parallel planes, previously used for elliptic and parabolic PDE, is adapted to study solutions of the Cauchy problem for Hamilton-Jacobi equations. This is possible in the framework of the theory of viscosity solutions, using the comparison theorem for such solutions as a kind of maximum principle. One of the main results states that if the initial data are nonnegative and compact supported, the Hamiltonian radial and the level sets expanding, then the level sets become asymptotically spherical as t → ∞, the convergence taking place in the Lipschitz norm.
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