CONTINUUM LIMIT OF p-BIHARMONIC EQUATIONS ON GRAPHS.
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| Title: | CONTINUUM LIMIT OF p-BIHARMONIC EQUATIONS ON GRAPHS. |
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| Authors: | SHI, KEHAN1 kshi@cjlu.edu.cn, BURGER, MARTIN2,3 martin.burger@desy.de |
| Source: | SIAM Journal on Mathematical Analysis. 2025, Vol. 57 Issue 4, p3784-3805. 22p. |
| Subjects: | Biharmonic equations, Graph theory, Random graphs, Point cloud, Neumann boundary conditions, Asymptotic analysis, Functional analysis |
| Abstract: | This paper studies the p-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph p-Laplacian from the perspective of hypergraphs. The asymptotic behavior of the solution is investigated for the random geometric graph when the number of data points goes to infinity. We show that the continuum limit is an appropriately weighted p-biharmonic equation with homogeneous Neumann boundary conditions. The result relies on the uniform Lp estimates for solutions and gradients of nonlocal and graph Poisson equations. The L∞ estimates of solutions are also obtained as a byproduct. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 188704933 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: CONTINUUM LIMIT OF p-BIHARMONIC EQUATIONS ON GRAPHS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22SHI%2C+KEHAN%22">SHI, KEHAN</searchLink><relatesTo>1</relatesTo><i> kshi@cjlu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22BURGER%2C+MARTIN%22">BURGER, MARTIN</searchLink><relatesTo>2,3</relatesTo><i> martin.burger@desy.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Mathematical+Analysis%22">SIAM Journal on Mathematical Analysis</searchLink>. 2025, Vol. 57 Issue 4, p3784-3805. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Biharmonic+equations%22">Biharmonic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Random+graphs%22">Random graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Point+cloud%22">Point cloud</searchLink><br /><searchLink fieldCode="DE" term="%22Neumann+boundary+conditions%22">Neumann boundary conditions</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+analysis%22">Asymptotic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper studies the p-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph p-Laplacian from the perspective of hypergraphs. The asymptotic behavior of the solution is investigated for the random geometric graph when the number of data points goes to infinity. We show that the continuum limit is an appropriately weighted p-biharmonic equation with homogeneous Neumann boundary conditions. The result relies on the uniform Lp estimates for solutions and gradients of nonlocal and graph Poisson equations. The L∞ estimates of solutions are also obtained as a byproduct. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Mathematical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/23M161639X Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 3784 Subjects: – SubjectFull: Biharmonic equations Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Random graphs Type: general – SubjectFull: Point cloud Type: general – SubjectFull: Neumann boundary conditions Type: general – SubjectFull: Asymptotic analysis Type: general – SubjectFull: Functional analysis Type: general Titles: – TitleFull: CONTINUUM LIMIT OF p-BIHARMONIC EQUATIONS ON GRAPHS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: SHI, KEHAN – PersonEntity: Name: NameFull: BURGER, MARTIN IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00361410 Numbering: – Type: volume Value: 57 – Type: issue Value: 4 Titles: – TitleFull: SIAM Journal on Mathematical Analysis Type: main |
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