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2019 A doubly nonlocal Laplace operator and its connection to the classical Laplacian
Petronela Radu, Kelsey Wells
J. Integral Equations Applications 31(3): 379-409 (2019). DOI: 10.1216/JIE-2019-31-3-379

Abstract

Motivated by the state-based peridynamic framework, we introduce a new nonlocal Laplacian that exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow for better representation of physical phenomena at different scales and in materials with different properties. We study mathematical properties of this state-based Laplacian, including connections with other nonlocal and local counterparts. Finally, we obtain explicit rates of convergence for this doubly nonlocal operator to the classical Laplacian as the radii for the horizons of interaction kernels shrink to zero.

Citation

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Petronela Radu. Kelsey Wells. "A doubly nonlocal Laplace operator and its connection to the classical Laplacian." J. Integral Equations Applications 31 (3) 379 - 409, 2019. https://doi.org/10.1216/JIE-2019-31-3-379

Information

Published: 2019
First available in Project Euclid: 2 November 2019

zbMATH: 07159849
MathSciNet: MR4027253
Digital Object Identifier: 10.1216/JIE-2019-31-3-379

Subjects:
Secondary: 74A45., 74B99

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 3 • 2019
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