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arXiv · 1812.03706

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

Marco Cirant·Alessandro Goffi
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Abstract

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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Marco Cirant, Alessandro Goffi. 2018-12-10. Lipschitz regularity for viscous Hamilton-Jacobi equations with $L^p$ terms. https://arxiv.org/abs/1812.03706

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