Lipschitz regularity for viscous Hamilton-Jacobi equations with L p terms
Cirant, Marco1 ; Goffi, Alessandro2
1 Dipartimento di Scienze Matematiche Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy
2 Gran Sasso Science Institute, viale Francesco Crispi 7, 67100 L'Aquila, Italy
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 757-784.
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We provide Lipschitz regularity for solutions to viscous time-dependent Hamilton-Jacobi equations with right-hand side belonging to Lebesgue spaces. Our approach is based on a duality method, and relies on the analysis of the regularity of the gradient of solutions to a dual (Fokker-Planck) equation. Here, the regularizing effect is due to the non-degenerate diffusion and coercivity of the Hamiltonian in the gradient variable.

DOI : 10.1016/j.anihpc.2020.01.006
Classification : 35F21, 35K55, 35B65
Mots-clés : Hamilton-Jacobi equations with unbounded data, Lipschitz regularity, Kardar-Parisi-Zhang, Adjoint method
Cirant, Marco 1 ; Goffi, Alessandro 2

1 Dipartimento di Scienze Matematiche Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/a, 43124 Parma, Italy
2 Gran Sasso Science Institute, viale Francesco Crispi 7, 67100 L'Aquila, Italy 
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     title = {Lipschitz regularity for viscous {Hamilton-Jacobi} equations with $L^p$ terms},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {757--784},
     publisher = {Elsevier},
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Cirant, Marco; Goffi, Alessandro. Lipschitz regularity for viscous Hamilton-Jacobi equations with $L^p$ terms. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 757-784. doi : 10.1016/j.anihpc.2020.01.006. http://archive.numdam.org/articles/10.1016/j.anihpc.2020.01.006/

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