Hyperbolicity of Minimizers and Regularity of Viscosity Solutions for a Random Hamilton–Jacobi Equation

Hyperbolicity of Minimizers and Regularity of Viscosity Solutions for a Random Hamilton–Jacobi... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

Hyperbolicity of Minimizers and Regularity of Viscosity Solutions for a Random Hamilton–Jacobi Equation

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
ISSN
0010-3616
eISSN
1432-0916
D.O.I.
10.1007/s00220-017-2919-5
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: May 30, 2017

References

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