Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient
Abstract
We obtain the comparison principle for discontinuous viscosity sub- and supersolutions of nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The nonlocal terms are integro-differential operators in L\'evy form, with general measures: -dependent, possibly degenerate and without any restriction on the order. The measures must satisfy a combined Wasserstein/Total Variation-continuity assumption, which is one of the weakest conditions used in the context of viscosity approach for this type of integro-differential PDEs. The proof relies on a regularizing effect due to the gradient growth. We present several examples of applications to PDEs with different types of nonlocal operators (measures with density, operators of variable order, L\'evy-It\^o operators).
Cite
@article{arxiv.2409.11124,
title = {Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient},
author = {Adina Ciomaga and Tri Minh Le and Olivier Ley and Erwin Topp},
journal= {arXiv preprint arXiv:2409.11124},
year = {2024}
}