Time fractional parabolic equations with partially SMO coefficients

Hongjie Dong; Doyoon Kim

doi:10.1016/j.jde.2023.10.006

Time fractional parabolic equations with partially SMO coefficients

Hongjie Dong
, Doyoon Kim^*

^*Corresponding author for this work

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in (t,x₁) for a^ij, 1≤i,j≤d, (i,j)≠(1,1). The coefficient a¹¹ is merely measurable locally either in t or x₁. As functions of the remaining variables, the coefficients have small mean oscillations. We consider mixed norm Sobolev spaces with Muckenhoupt weights. Our results generalize previous work on parabolic equations with time fractional derivatives to a much larger class of coefficients and solution spaces.

Original language	English
Pages (from-to)	759-808
Number of pages	50
Journal	Journal of Differential Equations
Volume	377
DOIs	https://doi.org/10.1016/j.jde.2023.10.006
Publication status	Published - 2023 Dec 25

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

Measurable coefficients
Muckenhoupt weights
Parabolic equations
Small mean oscillations
Time fractional derivative

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2023.10.006

Cite this

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title = "Time fractional parabolic equations with partially SMO coefficients",

abstract = "We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in (t,x1) for aij, 1≤i,j≤d, (i,j)≠(1,1). The coefficient a11 is merely measurable locally either in t or x1. As functions of the remaining variables, the coefficients have small mean oscillations. We consider mixed norm Sobolev spaces with Muckenhoupt weights. Our results generalize previous work on parabolic equations with time fractional derivatives to a much larger class of coefficients and solution spaces.",

keywords = "Measurable coefficients, Muckenhoupt weights, Parabolic equations, Small mean oscillations, Time fractional derivative",

author = "Hongjie Dong and Doyoon Kim",

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doi = "10.1016/j.jde.2023.10.006",

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T1 - Time fractional parabolic equations with partially SMO coefficients

AU - Dong, Hongjie

AU - Kim, Doyoon

PY - 2023/12/25

Y1 - 2023/12/25

N2 - We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in (t,x1) for aij, 1≤i,j≤d, (i,j)≠(1,1). The coefficient a11 is merely measurable locally either in t or x1. As functions of the remaining variables, the coefficients have small mean oscillations. We consider mixed norm Sobolev spaces with Muckenhoupt weights. Our results generalize previous work on parabolic equations with time fractional derivatives to a much larger class of coefficients and solution spaces.

AB - We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in (t,x1) for aij, 1≤i,j≤d, (i,j)≠(1,1). The coefficient a11 is merely measurable locally either in t or x1. As functions of the remaining variables, the coefficients have small mean oscillations. We consider mixed norm Sobolev spaces with Muckenhoupt weights. Our results generalize previous work on parabolic equations with time fractional derivatives to a much larger class of coefficients and solution spaces.

KW - Measurable coefficients

KW - Muckenhoupt weights

KW - Parabolic equations

KW - Small mean oscillations

KW - Time fractional derivative

UR - https://www.scopus.com/pages/publications/85174359479

U2 - 10.1016/j.jde.2023.10.006

DO - 10.1016/j.jde.2023.10.006

M3 - Article

AN - SCOPUS:85174359479

SN - 0022-0396

VL - 377

SP - 759

EP - 808

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Time fractional parabolic equations with partially SMO coefficients

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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