We show that for a large class of randomly kicked Hamilton–Jacobi equations, the unique global minimizer is almost surely hyperbolic. Furthermore, we prove that the unique forward and backward viscosity solutions, though in general only Lipshitz, are smooth in a neighborhood of the global minimizer. Related results in the one-dimensional case were obtained by E, Khanin et al. (Ann Math (2) 151(3):877–960, 2000). However, the methods in the above paper are purely one-dimensional and cannot be extended to the case of higher dimensions. Here we develop a completely different approach.
Communications in Mathematical Physics – Springer Journals
Published: May 30, 2017
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