Carleman inequalities and unique continuation for the polyharmonic operators

Eunhee Jeong; Yehyun Kwon; Sanghyuk Lee

doi:10.1016/j.jde.2023.12.004

Carleman inequalities and unique continuation for the polyharmonic operators

Eunhee Jeong
, Yehyun Kwon^*
, Sanghyuk Lee

^*Corresponding author for this work

Department of Mathematics Education

Research output: Contribution to journal › Journal article › peer-review

Abstract

We obtain a complete characterization of L^p−L^q Carleman estimates with weight e^v⋅x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig–Ruiz–Sogge. Consequently, we obtain new unique continuation properties of higher order Schrödinger equations relaxing the integrability assumption on the solution spaces.

Original language	English
Pages (from-to)	86-120
Number of pages	35
Journal	Journal of Differential Equations
Volume	385
DOIs	https://doi.org/10.1016/j.jde.2023.12.004
State	Published - 2024.03.15

Keywords

Carleman inequality
Polyharmonic operator
Unique continuation

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.jde.2023.12.004

Cite this

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title = "Carleman inequalities and unique continuation for the polyharmonic operators",

abstract = "We obtain a complete characterization of Lp−Lq Carleman estimates with weight ev⋅x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig–Ruiz–Sogge. Consequently, we obtain new unique continuation properties of higher order Schr{\"o}dinger equations relaxing the integrability assumption on the solution spaces.",

keywords = "Carleman inequality, Polyharmonic operator, Unique continuation",

author = "Eunhee Jeong and Yehyun Kwon and Sanghyuk Lee",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2024",

month = mar,

day = "15",

doi = "10.1016/j.jde.2023.12.004",

language = "English",

volume = "385",

pages = "86--120",

journal = "Journal of Differential Equations",

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T1 - Carleman inequalities and unique continuation for the polyharmonic operators

AU - Jeong, Eunhee

AU - Kwon, Yehyun

AU - Lee, Sanghyuk

PY - 2024/3/15

Y1 - 2024/3/15

N2 - We obtain a complete characterization of Lp−Lq Carleman estimates with weight ev⋅x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig–Ruiz–Sogge. Consequently, we obtain new unique continuation properties of higher order Schrödinger equations relaxing the integrability assumption on the solution spaces.

AB - We obtain a complete characterization of Lp−Lq Carleman estimates with weight ev⋅x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig–Ruiz–Sogge. Consequently, we obtain new unique continuation properties of higher order Schrödinger equations relaxing the integrability assumption on the solution spaces.

KW - Carleman inequality

KW - Polyharmonic operator

KW - Unique continuation

UR - https://www.scopus.com/pages/publications/85179787185

U2 - 10.1016/j.jde.2023.12.004

DO - 10.1016/j.jde.2023.12.004

M3 - Journal article

AN - SCOPUS:85179787185

SN - 0022-0396

VL - 385

SP - 86

EP - 120

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Carleman inequalities and unique continuation for the polyharmonic operators

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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