Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
Analysis of PDEs
2024-12-02 v6
Abstract
We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from -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.
Cite
@article{arxiv.2307.12932,
title = {Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method},
author = {Fabio Camilli and Alessandro Goffi and Cristian Mendico},
journal= {arXiv preprint arXiv:2307.12932},
year = {2024}
}