Lipschitz regularity for viscous Hamilton-Jacobi equations with L terms

@article{Cirant2018LipschitzRF,
  title={Lipschitz regularity for viscous Hamilton-Jacobi equations with L terms},
  author={Marco Cirant and Alessandro Goffi},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
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. 
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