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arXiv · 2403.03884

Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations

Espen R. Jakobsen·Artur Rutkowski
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Abstract

We survey some results on Lipschitz and Schauder regularity estimates for viscous Hamilton--Jacobi equations with subcritical Lévy diffusions. The Schauder estimates, along with existence of smooth solutions, are obtained with the help of a Duhamel formula and $L^1$ 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.

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Espen R. Jakobsen, Artur Rutkowski. 2024-03-06. Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations. https://arxiv.org/abs/2403.03884

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