Interpolation results for pathwise Hamilton-Jacobi equations
Analysis of PDEs
2021-01-19 v2
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, H\"older, 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.
Keywords
Cite
@article{arxiv.2007.02440,
title = {Interpolation results for pathwise Hamilton-Jacobi equations},
author = {Pierre-Louis Lions and Benjamin Seeger and Panagiotis Souganidis},
journal= {arXiv preprint arXiv:2007.02440},
year = {2021}
}
Comments
final version, to appear in IUMJ. Minor revisions, an open question has been answered with a counterexample of T. Tao