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Journal articles on the topic 'Nonlocal operators'

Author: Grafiati

Published: 9 March 2023

Last updated: 25 July 2025

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1

DU, QIANG, MAX GUNZBURGER, R. B. LEHOUCQ, and KUN ZHOU. "A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS." Mathematical Models and Methods in Applied Sciences 23, no. 03 (2013): 493–540. http://dx.doi.org/10.1142/s0218202512500546.

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A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoint operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators. The operators of the nonlocal calculus are used to define volu

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2

Lee, Hwi, and Qiang Du. "Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 1 (2020): 105–28. http://dx.doi.org/10.1051/m2an/2019053.

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Nonlocal gradient operators are prototypical nonlocal differential operators that are very important in the studies of nonlocal models. One of the simplest variational settings for such studies is the nonlocal Dirichlet energies wherein the energy densities are quadratic in the nonlocal gradients. There have been earlier studies to illuminate the link between the coercivity of the Dirichlet energies and the interaction strengths of radially symmetric kernels that constitute nonlocal gradient operators in the form of integral operators. In this work we adopt a different perspective and focus on

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3

Chen, Yufu, and Hongqing Zhang. "NONLOCAL SYMMETRIES AND NONLOCAL RECURSION OPERATORS." Acta Mathematica Scientia 21, no. 1 (2001): 103–8. http://dx.doi.org/10.1016/s0252-9602(17)30582-9.

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4

Lee, Duckhwan, and Herschel Rabitz. "Scaling of nonlocal operators." Physical Review A 32, no. 2 (1985): 877–82. http://dx.doi.org/10.1103/physreva.32.877.

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5

Lizama, Carlos, Marina Murillo-Arcila, and Alfred Peris. "Nonlocal operators are chaotic." Chaos: An Interdisciplinary Journal of Nonlinear Science 30, no. 10 (2020): 103126. http://dx.doi.org/10.1063/5.0018408.

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6

Boltachev, A. V. "On ellipticity of operators with shear mappings." Contemporary Mathematics. Fundamental Directions 69, no. 4 (2023): 565–77. http://dx.doi.org/10.22363/2413-3639-2023-69-4-565-577.

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The nonlocal boundary value problems are considered, in which the main operator and the operators in the boundary conditions include the differential operators and twisting operators. The de nition of the trajectory symbols for this class of problems is given. We show that the elliptic problems de ne the Fredholm operators in the corresponding Sobolev spaces. The ellipticity condition of such nonlocal boundary value problem is given.

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7

DI CECIO, G., and G. PAFFUTI. "SOME PROPERTIES OF RENORMALONS IN GAUGE THEORIES." International Journal of Modern Physics A 10, no. 10 (1995): 1449–63. http://dx.doi.org/10.1142/s0217751x95000693.

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We find the explicit operatorial form of renormalon type singularities in Abelian gauge theory. Local operators of dimension six take care of the first UV renormalon; nonlocal operators are needed for IR singularities. In the effective Lagrangian constructed with these operators nonlocal imaginary parts appearing in the usual perturbative expansion at large orders are canceled.

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8

Ishikawa, Tomomi. "Perturbative matching of continuum and lattice quasi-distributions." EPJ Web of Conferences 175 (2018): 06028. http://dx.doi.org/10.1051/epjconf/201817506028.

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Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically withWilson-type fermions. The matching is done for nonlocal quark bilinear operators with a straightWilson line in a spatial direction. We also investigate operator mixing in the renormalization and possible O(a) operators for the nonlocal operators based on a symmetry argument on lattice.

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9

Xu, Xin-Jian, and Chuan-Fu Yang. "Inverse nodal problem for nonlocal differential operators." Tamkang Journal of Mathematics 50, no. 3 (2019): 337–47. http://dx.doi.org/10.5556/j.tkjm.50.2019.3361.

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Inverse nodal problem consists in constructing operators from the given zeros of their eigenfunctions. The problem of differential operators with nonlocal boundary condition appears, e.g., in scattering theory, diffusion processes and the other applicable fields. In this paper, we consider a class of differential operators with nonlocal boundary condition, and show that the potential function can be determined by nodal data.

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10

Lou, Yifei, Xiaoqun Zhang, Stanley Osher, and Andrea Bertozzi. "Image Recovery via Nonlocal Operators." Journal of Scientific Computing 42, no. 2 (2009): 185–97. http://dx.doi.org/10.1007/s10915-009-9320-2.

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11

Shakhmurov, Veli B. "Degenerate Differential Operators with Parameters." Abstract and Applied Analysis 2007 (2007): 1–27. http://dx.doi.org/10.1155/2007/51410.

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The nonlocal boundary value problems for regular degenerate differential-operator equations with the parameter are studied. The principal parts of the appropriate generated differential operators are non-self-adjoint. Several conditions for the maximal regularity uniformly with respect to the parameter and the Fredholmness in Banach-valuedLp−spaces of these problems are given. In applications, the nonlocal boundary value problems for degenerate elliptic partial differential equations and for systems of elliptic equations with parameters on cylindrical domain are studied.

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12

Yin, Xiang Feng, Jin Ming Duan, Zhen Kuan Pan, Wei Bo Wei, and Guo Dong Wang. "Nonlocal TV-L1 Inpainting Model and its Augmented Lagrangian Algorithm." Applied Mechanics and Materials 644-650 (September 2014): 4630–36. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.4630.

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Nonlocal differential operators have been extensively applied to variational models for image restoration due to its texture-preserving capability. In this paper, we propose a nonlocal TV (total variation)-L1 model for texture image inpainting, which, technically, combines nonlocal operators for regularization term and L1 norm for data term. The former is used to regularize texture and the latter to preserve contrast of images. In addition, we develop augmented Lagrangian algorithm for proposed model by introducing nonlocal auxiliary variable and Lagrangian multiplier. Finally, extensive exper

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13

Chen, Wenxiong, Congming Li, and Yan Li. "A direct blowing-up and rescaling argument on nonlocal elliptic equations." International Journal of Mathematics 27, no. 08 (2016): 1650064. http://dx.doi.org/10.1142/s0129167x16500646.

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In this paper, we develop a direct blowing-up and rescaling argument for nonlinear equations involving nonlocal elliptic operators including the fractional Laplacian. Instead of using the conventional extension method introduced by Caffarelli and Silvestre to localize the problem, we work directly on the nonlocal operator. Using the defining integral, by an elementary approach, we carry on a blowing-up and rescaling argument directly on the nonlocal equations and thus obtain a priori estimates on the positive solutions. Based on this estimate and the Leray–Schauder degree theory, we establish

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14

D’Elia, Marta, Mamikon Gulian, Hayley Olson, and George Em Karniadakis. "Towards a unified theory of fractional and nonlocal vector calculus." Fractional Calculus and Applied Analysis 24, no. 5 (2021): 1301–55. http://dx.doi.org/10.1515/fca-2021-0057.

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Abstract Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fract

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15

Anguelov, Roumen, and Stephanus Marnus Stoltz. "Modelling of activator-inhibitor dynamics via nonlocal integral operators." Texts in Biomathematics 1 (December 28, 2017): 57. http://dx.doi.org/10.11145/texts.2017.12.233.

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This paper proposes application of nonlocal operators to represent the biological pattern formation mechanism of self-activation and lateral inhibition. The blue-green algae Anabaena is discussed as a model example. The patterns are determined by the kernels of the integrals representing the nonlocal operators. The emergence of patters when varying the size of the support of the kernels is numerically investigated.

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16

Ma, Zaizhong, Ying-Hwa Kuo, Bin Wang, Wan-Shu Wu, and Sergey Sokolovskiy. "Comparison of Local and Nonlocal Observation Operators for the Assimilation of GPS RO Data with the NCEP GSI System: An OSSE Study." Monthly Weather Review 137, no. 10 (2009): 3575–87. http://dx.doi.org/10.1175/2009mwr2809.1.

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Abstract In this study, an Observing System Simulation Experiment (OSSE) is performed to evaluate the performance of a nonlocal excess phase operator and a local refractivity operator for a GPS radio occultation (RO) sounding that passes through the eye of Hurricane Katrina as simulated by a high-resolution model, with significant horizontal refractivity gradients. Both observation operators are tested on the NCEP gridpoint statistical interpolation (GSI) data assimilation system at 12- and 36-km horizontal resolution. It is shown that the shape and magnitude of the analysis increments for sea

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17

Shapovalov, Alexander V., Anton E. Kulagin, and Andrey Yu Trifonov. "The Gross–Pitaevskii Equation with a Nonlocal Interaction in a Semiclassical Approximation on a Curve." Symmetry 12, no. 2 (2020): 201. http://dx.doi.org/10.3390/sym12020201.

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We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (curve) that evolves over time. The approach reduces the Cauchy problem for the nonlocal Gross–Pitaevskii equation to a similar problem for the associated linear equation. The geometric properties of the resulting solutions are related to Maslov’s complex germ, and the symmetry operators of the associated linear equation lead to the approximati

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18

Huang, Qiao, Jinqiao Duan, and Jiang-Lun Wu. "Maximum principles for nonlocal parabolic Waldenfels operators." Bulletin of Mathematical Sciences 09, no. 03 (2019): 1950015. http://dx.doi.org/10.1142/s1664360719500152.

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As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructing Markov processes with boundary conditions (in particular the construction with jumps). This work is devoted to prove the weak and strong maximum principles for ‘parabolic’ equations with nonlocal Waldenfels operators. Applications in stochastic differential equations with [Formula: see text]-stable Lévy processes are presented to illustrate the maximum principles.

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19

Kassmann, Moritz, and Ante Mimica. "Intrinsic scaling properties for nonlocal operators." Journal of the European Mathematical Society 19, no. 4 (2017): 983–1011. http://dx.doi.org/10.4171/jems/686.

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20

Dyda, Bartłomiej, and Moritz Kassmann. "Regularity estimates for elliptic nonlocal operators." Analysis & PDE 13, no. 2 (2020): 317–70. http://dx.doi.org/10.2140/apde.2020.13.317.

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21

Felsinger, Matthieu, and Moritz Kassmann. "Local Regularity for Parabolic Nonlocal Operators." Communications in Partial Differential Equations 38, no. 9 (2013): 1539–73. http://dx.doi.org/10.1080/03605302.2013.808211.

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22

Chaker, Jamil, and Moritz Kassmann. "Nonlocal operators with singular anisotropic kernels." Communications in Partial Differential Equations 45, no. 1 (2019): 1–31. http://dx.doi.org/10.1080/03605302.2019.1651335.

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23

Bogdan, Krzysztof, Tomasz Grzywny, Katarzyna Pietruska-Pałuba, and Artur Rutkowski. "Extension and trace for nonlocal operators." Journal de Mathématiques Pures et Appliquées 137 (May 2020): 33–69. http://dx.doi.org/10.1016/j.matpur.2019.09.005.

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24

Geyer, Bodo, and Markus Lazar. "Nonlocal LC-operators of definite twist." Nuclear Physics B - Proceedings Supplements 90 (December 2000): 28–30. http://dx.doi.org/10.1016/s0920-5632(00)00866-5.

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25

Kravchenko, K. V. "Differential operators with nonlocal boundary conditions." Differential Equations 36, no. 4 (2000): 517–23. http://dx.doi.org/10.1007/bf02754246.

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26

Mustafa, M. M., and M. W. Kermode. "The nonlocal tensor operatorS 12 N (?, ??)." Few-Body Systems 11, no. 2-3 (1991): 83–88. http://dx.doi.org/10.1007/bf01318553.

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27

Bogdan, Krzysztof, Paweł Sztonyk, and Victoria Knopova. "Heat Kernel of Anisotropic Nonlocal Operators." Documenta Mathematica 25 (2020): 1–54. http://dx.doi.org/10.4171/dm/736.

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28

Xu, Xin-Jian, and Chuan-Fu Yang. "Trace formula for nonlocal differential operators." Indian Journal of Pure and Applied Mathematics 50, no. 4 (2019): 1107–14. http://dx.doi.org/10.1007/s13226-019-0378-8.

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29

Albeverio, Sergio, and Leonid Nizhnik. "Schrödinger operators with nonlocal point interactions." Journal of Mathematical Analysis and Applications 332, no. 2 (2007): 884–95. http://dx.doi.org/10.1016/j.jmaa.2006.10.070.

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30

Zhang, Xicheng. "Fundamental Solutions of Nonlocal Hörmander’s Operators." Communications in Mathematics and Statistics 4, no. 3 (2016): 359–402. http://dx.doi.org/10.1007/s40304-016-0090-5.

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31

Felsinger, Matthieu, Moritz Kassmann, and Paul Voigt. "The Dirichlet problem for nonlocal operators." Mathematische Zeitschrift 279, no. 3-4 (2014): 779–809. http://dx.doi.org/10.1007/s00209-014-1394-3.

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32

Nyeo, Su-Long. "Anomalous dimensions of nonlocal baryon operators." Zeitschrift für Physik C Particles and Fields 54, no. 4 (1992): 615–19. http://dx.doi.org/10.1007/bf01559489.

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33

Correa, Ernesto, and Arturo de Pablo. "Nonlocal operators of order near zero." Journal of Mathematical Analysis and Applications 461, no. 1 (2018): 837–67. http://dx.doi.org/10.1016/j.jmaa.2017.12.011.

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34

Buoninfante, Luca, Gaetano Lambiase, and Masahide Yamaguchi. "Enlarging local symmetries: A nonlocal Galilean model." International Journal of Geometric Methods in Modern Physics 17, supp01 (2020): 2040009. http://dx.doi.org/10.1142/s0219887820400095.

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We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level uni

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35

Ruzhansky, Michael, Niyaz Tokmagambetov, and Berikbol T. Torebek. "On a non–local problem for a multi–term fractional diffusion-wave equation." Fractional Calculus and Applied Analysis 23, no. 2 (2020): 324–55. http://dx.doi.org/10.1515/fca-2020-0016.

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AbstractThis paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal conditions. Several examples of the settings where our nonlocal problems are applicable are given. The results for the discrete spectrum are also applied to treat the case of general homogeneous hypoelliptic left-invariant differential operators on general graded Lie groups, by using the representation theory of the group. For all these problems, we show

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36

Piatnitski, A., V. Sloushch, T. Suslina, and E. Zhizhina. "On operator estimates in homogenization of nonlocal operators of convolution type." Journal of Differential Equations 352 (April 2023): 153–88. http://dx.doi.org/10.1016/j.jde.2022.12.036.

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37

Kan, Xingyu, Yiwei Wang, Jiale Yan, and Renfang Huang. "The Comparisons Between Peridynamic Differential Operators and Nonlocal Differential Operators." International Conference on Computational & Experimental Engineering and Sciences 25, no. 2 (2023): 1–2. http://dx.doi.org/10.32604/icces.2023.09937.

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38

Maltsev, Andrei Ya. "On the compatible weakly nonlocal Poisson brackets of hydrodynamic type." International Journal of Mathematics and Mathematical Sciences 32, no. 10 (2002): 587–614. http://dx.doi.org/10.1155/s0161171202202069.

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We consider the pairs of general weakly nonlocal Poisson brackets of hydrodynamic type (Ferapontov brackets) and the corresponding integrable hierarchies. We show that, under the requirement of the nondegeneracy of the corresponding first pseudo-Riemannian metricg(0) νμand also some nondegeneracy requirement for the nonlocal part, it is possible to introduce a canonical set of integrable hierarchies based on the Casimirs, momentum functional and some canonical Hamiltonian functions. We prove also that all the higher positive Hamiltonian operators and the negative symplectic forms

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39

Eckardt, Maria, Kevin J. Painter, Christina Surulescu, and Anna Zhigun. "Nonlocal and local models for taxis in cell migration: a rigorous limit procedure." Journal of Mathematical Biology 81, no. 6-7 (2020): 1251–98. http://dx.doi.org/10.1007/s00285-020-01536-4.

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AbstractA rigorous limit procedure is presented which links nonlocal models involving adhesion or nonlocal chemotaxis to their local counterparts featuring haptotaxis and classical chemotaxis, respectively. It relies on a novel reformulation of the involved nonlocalities in terms of integral operators applied directly to the gradients of signal-dependent quantities. The proposed approach handles both model types in a unified way and extends the previous mathematical framework to settings that allow for general solution-dependent coefficient functions. The previous forms of nonlocal operators a

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40

Kim, Yong-Cheol. "Nonlocal Harnack inequalities for nonlocal Schrödinger operators with A1-Muckenhoupt potentials." Journal of Mathematical Analysis and Applications 507, no. 1 (2022): 125746. http://dx.doi.org/10.1016/j.jmaa.2021.125746.

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41

Fernández Bonder, Julián, Antonella Ritorto, and Ariel Martin Salort. "A class of shape optimization problems for some nonlocal operators." Advances in Calculus of Variations 11, no. 4 (2018): 373–86. http://dx.doi.org/10.1515/acv-2016-0065.

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AbstractIn this work we study a family of shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze the transition from nonlocal to local state equations.

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42

Zhou, Mian, and Yong Zhou. "Existence of Mild Solutions for Fractional Integrodifferential Equations with Hilfer Derivatives." Mathematics 13, no. 9 (2025): 1369. https://doi.org/10.3390/math13091369.

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In this paper, we study the existence of solutions for fractional integrodifferential equations with Hilfer derivatives. We establish some new existence theorems for mild solutions by using Schaefer’s fixed-point theorem, a measure of noncompactness, and the resolvent operators associated with almost sectorial operators. Our results improve and extend many known results in the relevant references by removing some strong assumptions. Furthermore, we propose new nonlocal initial conditions for Hilfer evolution equations and study the existence of mild solutions to nonlocal problems.

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43

Tanha, Nayereh, Behrouz Parsa Moghaddam, and Mousa Ilie. "Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators." Computation 12, no. 1 (2024): 14. http://dx.doi.org/10.3390/computation12010014.

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This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and

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44

Cooper, Randolph G. "A Note on the Regularity of the Solutions to Two Variational Inequalities Involving a Pseudodifferential Operator." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–8. http://dx.doi.org/10.1155/2007/95738.

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The regularity of solutions to variational inequalities involving local operators has been studied extensively. Less attention has been paid to those involving nonlocal pseudodifferential operators. We present two regularity results for such problems.

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45

Fan, Zhenbin, and Gisèle Mophou. "Nonlocal Problems for Fractional Differential Equations via Resolvent Operators." International Journal of Differential Equations 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/490673.

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We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.

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46

Usmanov, Kairat, Batirkhan Turmetov, and Kulzina Nazarova. "On the Solvability of Some Boundary Value Problems for the Nonlocal Poisson Equation with Boundary Operators of Fractional Order." Fractal and Fractional 6, no. 6 (2022): 308. http://dx.doi.org/10.3390/fractalfract6060308.

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In this paper, in the class of smooth functions, integration and differentiation operators connected with fractional conformable derivatives are introduced. The mutual reversibility of these operators is proved, and the properties of these operators in the class of smooth functions are studied. Using transformations generalizing involutive transformations, a nonlocal analogue of the Laplace operator is introduced. For the corresponding nonlocal analogue of the Poisson equation, the solvability of some boundary value problems with fractional conformable derivatives is studied. For the problems

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47

Izvarina, N. R. "ON THE SYMBOL OF NONLOCAL OPERATORS ASSOCIATED WITH A PARABOLIC DIFFEOMORPHISM." Eurasian Mathematical Journal 9, no. 2 (2018): 34–43. http://dx.doi.org/10.32523/2077-9879-2018-9-2-34-43.

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48

de Angelis, Fabio. "Evolutive Laws and Constitutive Relations in Nonlocal Viscoplasticity." Applied Mechanics and Materials 152-154 (January 2012): 990–96. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.990.

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In the present work the evolutive laws and the constitutive relations for a model of nonlocal viscoplasticity are analyzed. Nonlocal dissipative variables and suitable regularization operators are adopted. The proposed model is developed within the framework of the generalized standard material model. Suitable forms of the elastic and dissipative viscoplastic potentials are defined and the associated constitutive relations are specialized. The evolutive laws for the proposed nonlocal viscoplastic model are presented in a general form which can be suitably specialized in order to include differ

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49

Shakhmurov, Veli B. "Maximal regular boundary value problems in Banach-valued function spaces and applications." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–26. http://dx.doi.org/10.1155/ijmms/2006/92134.

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The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valuedLp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value p

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50

d’Avenia, Pietro, and Marco Squassina. "Ground states for fractional magnetic operators." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 1 (2017): 1–24. http://dx.doi.org/10.1051/cocv/2016071.

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We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness.

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