Interpolation results for pathwise Hamilton-Jacobi equations

2020/07/05 by Pierre‐Louis Lions, Lions, Pierre-Louis, Benjamin Seeger +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2007.02440

openalex publication_date 2020/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the interplay between the regularity of paths and Hamiltonians in the theory of pathwise Hamilton-Jacobi equations with the use of interpolation methods. The regularity of the paths is measured with respect to Sobolev, Besov, Hölder, and variation norms, and criteria for the Hamiltonians are presented in terms of both regularity and structure. We also explore various properties of functions that are representable as the difference of convex functions, the largest space of Hamiltonians for which the equation is well-posed for all continuous paths. Finally, we discuss some open problems and conjectures.

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