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Q. Du and J. M. Scott, "Weighted nonlocal operators and their applications in semi-supervised learning." Submitted. arXiv Preprint
E. Zhang, J. M. Scott, Q. Du, M. Porter, "Ginzburg-Landau Functionals in the Large-Graph Limit." Submitted. arXiv Preprint
J.M. Scott, "The Fractional Lame-Navier Equation: Appearances, Properties and Applications." Submitted. arXiv Preprint
Q. Du, J. M. Scott and X. Tian, "Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems." To appear in Mathematics of Computation. arXiv Preprint
J. M. Scott and Q. Du, "Nonlocal boundary-value problems with local boundary conditions II: Green's identities and regularity of solutions." SIAM Journal on Mathematical Analysis, 57(1) (2025), 404-451. Online Version
Q. Du, J. M. Scott and Z. Xu, "Ohta-Kawasaki energy for amphiphiles: asymptotics and phase-field simulations." Nonlinear Analysis, 250 (2025), 113665. Online Version
J. M. Scott and Q. Du, "Nonlocal boundary-value problems with local boundary conditions I: function spaces and variational principles." SIAM Journal on Mathematical Analysis, 56(3) (2024), 4185-4222. Online Version
T. Mengesha and J. M. Scott, "Linearization and localization of nonconvex functionals motivated by nonlinear peridynamic models." Continuum Mechanics and Thermodynamics, 36 (2024), 795-824. Online Version
Y. Gao and J. M. Scott, "Existence and uniqueness of solutions to the Peierls-Nabarro model in anisotropic media." Nonlinearity, 37(2) (2024), 025010. Online Version
D. Harutyunyan, T. Mengesha, H. Mikayelyan and J. M. Scott, "Fractional Korn's inequalities without boundary conditions." Mathematics and Mechanics of Complex Systems, 11(4) (2023), 795-824. Online Version
Q. Du, K. Huang, W. Shen and J. M. Scott, "A space-time nonlocal traffic flow model: relaxation representation and local limit." Discrete and Continuous Dynamical Systems, 43(9) (2023), 3456-3484. Online Version
T. Mengesha and J. M. Scott, "A Note on Estimates of Level Sets and Their Role in Demonstrating Regularity of Solutions to Nonlocal Double-Phase Equations." A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models: Proceedings of the 50th John H. Barrett Memorial Lectures. Springer International Publishing (2023), 253-293. Online Version
A. Schikorra and J. M. Scott, "Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note." Studia Mathematica, 269 (2023), 241-260. Online Version
M. D' Elia, M. Gulian, T. Mengesha and J. M. Scott, "Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition." Fractional Calculus and Applied Analysis, 25 (2022), 2488–2531. Online Version
J. M. Scott and T. Mengesha, "Self-Improving inequalities for bounded weak solutions to nonlocal double phase equations." Communications on Pure and Applied Analysis, 21(1) (2022), 183-212. Online Version
T. Mengesha and J. Scott, "A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations." Communications in Mathematical Sciences, 20(2) (2022), 405-423. Online Version
J. Scott and T. Mengesha, "Asymptotic Analysis of Solutions to a Coupled System of Nonlocal Equations with Oscillatory Coefficients." Multiscale Modeling & Simulation, 18(4) (2020), 1462-1488. Online Version
T. Mengesha and J. Scott, "The Solvability of a Strongly-Coupled Nonlocal System of Equations." Journal of Mathematical Analysis and Applications, 486(2) (2020), article 123919. Online Version
M. Kassmann, T. Mengesha, and J. Scott, "Solvability of Nonlocal Systems Related to Peridynamics." Communications on Pure & Applied Analysis, 18 (2019), pp. 1303-1332. Online Version
J. Scott and T. Mengesha, "A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics." SIAM Journal on Mathematical Analysis, 51 (2019), pp. 86-109. Online Version
J. Scott and T. Mengesha, "A Fractional Korn-Type Inequality." Discrete and Continuous Dynamical Systems, 39(6) (2019), pp. 3315-3343. Online Version
J. Scott, M. P. Laiu, and C. D. Hauck, "Analysis of the Zero Relaxation Limit of Systems of Hyperbolic Balance Laws with Random Initial Data." SIAM/ASA Journal of Uncertainty Quantification, 7(3) (2019), pp. 806-837. Online Version. A version with supplementary material is located here.