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

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arxiv 2307.12932 v6 pith:4SCVG2YG submitted 2023-07-24 math.AP

Fabio Camilli , Alessandro Goffi , Cristian Mendico This is my paper · ORCID
classification math.AP
keywords equationshamilton-jacobiseveraladjointadvection-diffusionapproachapproximationcareful
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations

    math.AP 2025-06 conditional novelty 8.0 of 10

    Vanishing viscosity for uniformly convex Hamilton-Jacobi equations converges at the optimal rate O(epsilon log epsilon), improving the old O(sqrt(epsilon)) bound.

  2. Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations

    math.AP 2025-02 conditional novelty 7.0 of 10

    The vanishing-viscosity error for quadratic Hamilton-Jacobi equations is of order ε log ε (not √ε), sharp in every dimension, with leading constant d/2.

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