Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911790196064256 |
|---|---|
| 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 |