A Priori Lipschitz Estimates for Solutions of Local and Nonlocal Hamilton-Jacobi Equations with Ornstein-Uhlenbeck Operator - Archive ouverte HAL Access content directly
Journal Articles Revista Matemática Iberoamericana Year : 2019

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

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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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Dates and versions

hal-01515409 , version 1 (27-04-2017)

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Cite

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, 2019, 35 (5), pp.1415-1449. ⟨10.4171/RMI/1093⟩. ⟨hal-01515409⟩
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