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arXiv · 2307.12932

Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method

Fabio Camilli·Alessandro Goffi·Cristian Mendico
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Abstract

We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theorems. Our approach is based on duality techniques \`a la Evans and a careful study of advection-diffusion equations. The optimality of the results is discussed by several examples.

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Fabio Camilli, Alessandro Goffi, Cristian Mendico. 2023-07-24. Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method. https://arxiv.org/abs/2307.12932

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