A priori Lipschitz estimates for solutions of local and nonlocal Hamilton–Jacobi equations with Ornstein–Uhlenbeck operato

• Emmanuel Chasseigne ^[2] ; Olivier Ley ^[1] ; Thi Tuyen Nguyen ^[3]
  1. [1] Institut National des Sciences Appliquées de Rennes

     Institut National des Sciences Appliquées de Rennes

     Arrondissement de Rennes, Francia

     
  2. [2] Université de Tours
  3. [3] Università di Padova

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 5, 2019, págs. 1415-1449
• Idioma: inglés
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• Resumen

  • We establish a priori Lipschitz estimates for unbounded solutions of second-order Hamilton–Jacobi equations in RN in presence of an Ornstein–Uhlenbeck drift. We generalize the results obtained by Fujita, Ishii and 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.