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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01515409
Contributeur : Olivier Ley <>
Soumis le : jeudi 27 avril 2017 - 14:33:46
Dernière modification le : lundi 25 septembre 2017 - 18:52:02
Document(s) archivé(s) le : vendredi 28 juillet 2017 - 13:10:12

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  • HAL Id : hal-01515409, version 1
  • ARXIV : 1705.00921

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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. 2017. 〈hal-01515409〉

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