Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations
Analysis of PDEs
2024-03-07 v1
Abstract
We survey some results on Lipschitz and Schauder regularity estimates for viscous Hamilton--Jacobi equations with subcritical L\'evy diffusions. The Schauder estimates, along with existence of smooth solutions, are obtained with the help of a Duhamel formula and bounds on the spatial derivatives of the heat kernel. Our results cover very general nonlocal and mixed local-nonlocal diffusions, including strongly anisotropic, nonsymmetric, mixed order, and spectrally one-sided models.
Keywords
Cite
@article{arxiv.2403.03884,
title = {Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations},
author = {Espen R. Jakobsen and Artur Rutkowski},
journal= {arXiv preprint arXiv:2403.03884},
year = {2024}
}