Towards a Schauder theory for fractional viscous Hamilton–Jacobi equations
arxiv(2024)
摘要
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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