Higher Hölder regularity for a subquadratic nonlocal parabolic equation

Prashanta Garain; Erik Lindgren; Alireza Tavakoli

doi:10.1016/j.jde.2024.11.024

Higher Hölder regularity for a subquadratic nonlocal parabolic equation

Prashanta Garain
, Erik Lindgren
, Alireza Tavakoli

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation ∂_tu+(−Δ_p)^su=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≥2.

Original language	English
Pages (from-to)	253-290
Number of pages	38
Journal	Journal of Differential Equations
Volume	419
DOIs	https://doi.org/10.1016/j.jde.2024.11.024
State	Published - 25 Feb 2025
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2024.11.024

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title = "Higher H{\"o}lder regularity for a subquadratic nonlocal parabolic equation",

abstract = "In this paper, we are concerned with the H{\"o}lder regularity for solutions of the nonlocal evolutionary equation ∂tu+(−Δp)su=0. Here, (−Δp)s is the fractional p-Laplacian, 0",

author = "Prashanta Garain and Erik Lindgren and Alireza Tavakoli",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2025",

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doi = "10.1016/j.jde.2024.11.024",

language = "English",

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T1 - Higher Hölder regularity for a subquadratic nonlocal parabolic equation

AU - Garain, Prashanta

AU - Lindgren, Erik

AU - Tavakoli, Alireza

PY - 2025/2/25

Y1 - 2025/2/25

N2 - In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation ∂tu+(−Δp)su=0. Here, (−Δp)s is the fractional p-Laplacian, 0

AB - In this paper, we are concerned with the Hölder regularity for solutions of the nonlocal evolutionary equation ∂tu+(−Δp)su=0. Here, (−Δp)s is the fractional p-Laplacian, 0

UR - https://www.scopus.com/pages/publications/85210414430

U2 - 10.1016/j.jde.2024.11.024

DO - 10.1016/j.jde.2024.11.024

M3 - Article

AN - SCOPUS:85210414430

SN - 0022-0396

VL - 419

SP - 253

EP - 290

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Higher Hölder regularity for a subquadratic nonlocal parabolic equation

Abstract

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