Calculus of Variations and Geometric Measure Theory
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M. Cirant - A. Goffi

Lipschitz regularity for viscous Hamilton-Jacobi equations with $L^p$ terms

created by goffi on 01 Jan 2019
modified on 09 Jun 2020


Published Paper

Inserted: 1 jan 2019
Last Updated: 9 jun 2020

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 37
Number: 4
Pages: 757-784
Year: 2020
Doi: 10.1016/j.anihpc.2020.01.006

ArXiv: 1812.03706 PDF


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.

Keywords: Lipschitz regularity, adjoint method, Hamilton-Jacobi equations with unbounded data, Kardar-Parisi-Zhang


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