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

Fuente: arXiv
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Main Authors: Jakobsen, Espen R., Rutkowski, Artur
Format: Preprint
Published: 2024
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author Jakobsen, Espen R.
Rutkowski, Artur
author_facet Jakobsen, Espen R.
Rutkowski, Artur
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_03884
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations
Jakobsen, Espen R.
Rutkowski, Artur
Analysis of PDEs
49L12, 35S10, 35A01, 35K08, 45K05, 35K61, 35B65, 35A09
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.
title Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations
topic Analysis of PDEs
49L12, 35S10, 35A01, 35K08, 45K05, 35K61, 35B65, 35A09
url https://arxiv.org/abs/2403.03884