$C^1$-estimates in nonlocal parabolic problems

Under a minimal tail condition, local weak solutions to a class of nonlinear nonlocal parabolic equations modeled on the fractional heat equation possess continuous spatial derivatives.

Authors

Verena Bögelein (ORCID: https://orcid.org/0000-0002-5646-2023)
Naian Liao (ORCID: https://orcid.org/0000-0003-2378-148X)
Calvin Stanko (ORCID: https://orcid.org/0009-0000-8668-3049)

Publication Details

Journal: arXiv (Cornell University)
Published: 2026-11-02
DOI: https://doi.org/10.48550/arxiv.2611.03122
Primary Topic: Nonlinear Partial Differential Equations
Type: preprint

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preprint

$C^1$-estimates in nonlocal parabolic problems

Verena Bögelein, Naian Liao, Calvin Stanko

Nov 2, 2026

arXiv (Cornell University)

Nonlinear Partial Differential Equations

preprint

$C^1$-estimates in nonlocal parabolic problems

Verena Bögelein, Naian Liao, Calvin Stanko

November 2, 2026preprint en

Abstract

Under a minimal tail condition, local weak solutions to a class of nonlinear nonlocal parabolic equations modeled on the fractional heat equation possess continuous spatial derivatives.

arXiv (Cornell University)

Nonlinear Partial Differential Equations

DOI Open Access PDF OpenAlex

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$C^1$-estimates in nonlocal parabolic problems — Verena Bögelein, Naian Liao, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS