Maximal regularity of parabolic equations associated with a discrete Laplacian

The Anh Bui

doi:10.1016/j.jde.2023.07.043

Maximal regularity of parabolic equations associated with a discrete Laplacian

The Anh Bui

School of Mathematical and Physical Sciences

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

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Abstract

Let Δ_d be the discrete Laplacian defined on Z^d by setting Δ_df(n→)=∑j=1d−[f(n→+e→_j)+f(n→−e→_j)−2f(n→)],n→∈Z^d, where {e→_j:j=1,…,d} is the standard basis for R^d. In this paper, we prove weighted mixed norm estimates and end-point estimates for the maximal regularity of the discrete parabolic equation {u_t+Δ_du=f,t∈[0,T)u(0,⋅)=0, where T∈(0,∞).

Original language	English
Pages (from-to)	277-303
Number of pages	27
Journal	Journal of Differential Equations
Volume	375
DOIs	https://doi.org/10.1016/j.jde.2023.07.043
Publication status	Published - Dec 2023

Bibliographical note

Copyright © 2023 The Author(s). Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Besov space
Discrete Laplacian
Maximal regularity
Parabolic equation

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10.1016/j.jde.2023.07.043Licence: CC BY

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Cite this

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title = "Maximal regularity of parabolic equations associated with a discrete Laplacian",

abstract = "Let Δd be the discrete Laplacian defined on Zd by setting Δdf(n→)=∑j=1d−[f(n→+e→j)+f(n→−e→j)−2f(n→)],n→∈Zd, where {e→j:j=1,…,d} is the standard basis for Rd. In this paper, we prove weighted mixed norm estimates and end-point estimates for the maximal regularity of the discrete parabolic equation {ut+Δdu=f,t∈[0,T)u(0,⋅)=0, where T∈(0,∞).",

keywords = "Besov space, Discrete Laplacian, Maximal regularity, Parabolic equation",

author = "Bui, {The Anh}",

note = "Copyright {\textcopyright} 2023 The Author(s). Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.",

year = "2023",

month = dec,

doi = "10.1016/j.jde.2023.07.043",

language = "English",

volume = "375",

pages = "277--303",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Maximal regularity of parabolic equations associated with a discrete Laplacian

AU - Bui, The Anh

N1 - Copyright © 2023 The Author(s). Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2023/12

Y1 - 2023/12

N2 - Let Δd be the discrete Laplacian defined on Zd by setting Δdf(n→)=∑j=1d−[f(n→+e→j)+f(n→−e→j)−2f(n→)],n→∈Zd, where {e→j:j=1,…,d} is the standard basis for Rd. In this paper, we prove weighted mixed norm estimates and end-point estimates for the maximal regularity of the discrete parabolic equation {ut+Δdu=f,t∈[0,T)u(0,⋅)=0, where T∈(0,∞).

AB - Let Δd be the discrete Laplacian defined on Zd by setting Δdf(n→)=∑j=1d−[f(n→+e→j)+f(n→−e→j)−2f(n→)],n→∈Zd, where {e→j:j=1,…,d} is the standard basis for Rd. In this paper, we prove weighted mixed norm estimates and end-point estimates for the maximal regularity of the discrete parabolic equation {ut+Δdu=f,t∈[0,T)u(0,⋅)=0, where T∈(0,∞).

KW - Besov space

KW - Discrete Laplacian

KW - Maximal regularity

KW - Parabolic equation

UR - http://www.scopus.com/inward/record.url?scp=85168936268&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP220100285

U2 - 10.1016/j.jde.2023.07.043

DO - 10.1016/j.jde.2023.07.043

M3 - Article

AN - SCOPUS:85168936268

SN - 0022-0396

VL - 375

SP - 277

EP - 303

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Maximal regularity of parabolic equations associated with a discrete Laplacian

Abstract

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Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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Maximal regularity of parabolic equations associated with a discrete Laplacian

Abstract

Bibliographical note

Keywords

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DP22: Harmonic analysis of Laplacians in curved spaces

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