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

2017/05/02 by Emmanuel Chasseigne, Chasseigne, Emmanuel, Olivier Ley +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1705.00921

openalex publication_date 2017/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a priori Lipschitz estimates for unbounded solutions of\nsecond-order Hamilton-Jacobi equations in R^N in presence of an\nOrnstein-Uhlenbeck drift. We generalize the results obtained by Fujita, Ishii\n & Loreti (2006) in several directions. The first one is to consider more\ngeneral operators. We first replace the Laplacian by a general diffusion matrix\nand then consider a nonlocal integro-differential operator of fractional\nLaplacian type. The second kind of extension is to deal with more general\nHamiltonians which are merely sublinear. These results are obtained for both\ndegenerate and nondegenerate equations.\n

Citations

• Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems

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• Regularity theory for degenerate fully nonlinear nonlocal equations with a Hamiltonian term

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