Pointwise convergence for the elastic wave equation

Chu Hee Cho; Seongyeon Kim; Yehyun Kwon; Ihyeok Seo

doi:10.1007/s00013-022-01757-7

Pointwise convergence for the elastic wave equation

Chu Hee Cho
, Seongyeon Kim
, Yehyun Kwon
, Ihyeok Seo

Department of Mathematics

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

Abstract

We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every line to the initial data almost everywhere whenever the initial regularity is greater than one half. We show this is almost optimal.

Original language	English
Pages (from-to)	303-310
Number of pages	8
Journal	Archiv der Mathematik
Volume	119
Issue number	3
DOIs	https://doi.org/10.1007/s00013-022-01757-7
State	Published - Sep 2022

Keywords

Elastic wave equation
Maximal estimate
Pointwise convergence

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10.1007/s00013-022-01757-7

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title = "Pointwise convergence for the elastic wave equation",

abstract = "We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every line to the initial data almost everywhere whenever the initial regularity is greater than one half. We show this is almost optimal.",

keywords = "Elastic wave equation, Maximal estimate, Pointwise convergence",

author = "Cho, \{Chu Hee\} and Seongyeon Kim and Yehyun Kwon and Ihyeok Seo",

note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.",

year = "2022",

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doi = "10.1007/s00013-022-01757-7",

language = "English",

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AU - Cho, Chu Hee

AU - Kim, Seongyeon

AU - Kwon, Yehyun

AU - Seo, Ihyeok

PY - 2022/9

Y1 - 2022/9

N2 - We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every line to the initial data almost everywhere whenever the initial regularity is greater than one half. We show this is almost optimal.

AB - We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every line to the initial data almost everywhere whenever the initial regularity is greater than one half. We show this is almost optimal.

KW - Elastic wave equation

KW - Maximal estimate

KW - Pointwise convergence

UR - https://www.scopus.com/pages/publications/85135825978

U2 - 10.1007/s00013-022-01757-7

DO - 10.1007/s00013-022-01757-7

M3 - Article

AN - SCOPUS:85135825978

SN - 0003-889X

VL - 119

SP - 303

EP - 310

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 3

ER -

Pointwise convergence for the elastic wave equation

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