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A Priori Lipschitz Estimates for Solutions of Local and Nonlocal Hamilton-Jacobi Equations with Ornstein-Uhlenbeck Operator

Abstract : We establish a priori Lipschitz estimates for unbounded solutions of second-order Hamilton-Jacobi equations in R^N in presence of an Ornstein-Uhlenbeck drift. We generalize the results obtained by Fujita, Ishii & Loreti (2006) in several directions. The first one is to consider more general operators. We first replace the Laplacian by a general diffusion matrix and then consider a nonlocal integro-differential operator of fractional Laplacian type. The second kind of extension is to deal with more general Hamiltonians which are merely sublinear. These results are obtained for both degenerate and nondegenerate equations.
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https://hal.archives-ouvertes.fr/hal-01515409
Contributor : Olivier Ley <>
Submitted on : Thursday, April 27, 2017 - 2:33:46 PM
Last modification on : Monday, July 6, 2020 - 3:38:11 PM
Long-term archiving on: : Friday, July 28, 2017 - 1:10:12 PM

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Emmanuel Chasseigne, Olivier Ley, Thi-Tuyen Nguyen. A Priori Lipschitz Estimates for Solutions of Local and Nonlocal Hamilton-Jacobi Equations with Ornstein-Uhlenbeck Operator. Revista Matemática Iberoamericana, European Mathematical Society, 2019, 35 (5), pp.1415-1449. ⟨10.4171/RMI/1093⟩. ⟨hal-01515409⟩

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