次二次非局部抛物方程的更高Hölder正则性

IF 2.3 2区数学 Q1 MATHEMATICS Journal of Differential Equations Pub Date : 2025-02-25 Epub Date: 2024-11-29 DOI:10.1016/j.jde.2024.11.024

Prashanta Garain , Erik Lindgren , Alireza Tavakoli

引用次数: 0

摘要

在本文中，我们关注非局部进化方程∂tu+(−Δp)su=0解的Hölder正则性。这里，（−Δp）s是分数阶p-拉普拉斯式，0<s<；1和1<；p<2。我们用显式的Hölder指数建立Hölder正则性。我们还包括有界非齐次方程。在某些情况下，得到的Hölder指数几乎是尖锐的。当p≥2时，我们的结果补充了先前的超二次情形的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Higher Hölder regularity for a subquadratic nonlocal parabolic equation

In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation

\partial_{t} u + {(- Δ_{p})}^{s} u = 0 .

Here,

{(- Δ_{p})}^{s}

is the fractional p-Laplacian,

0 < s < 1

and

1 < p < 2

. We establish Hölder regularity with explicit Hölder exponents. We also include the inhomogeneous equation with a bounded inhomogeneity. In some cases, the obtained Hölder exponents are almost sharp. Our results complement the previous results for the superquadratic case when

p \geq 2

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics

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