Inserted: 1 jan 2019
Last Updated: 9 jun 2020
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
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