Research Publications

A Diffuse Domain Approximation with Transmission-Type Boundary Conditions II: Gamma--Convergence, (with T. Luong, S. M. Wise, M. H. Wong ). International Journal of Numerical Analysis and Modeling, Vol 22, Num 5, Pages 728-744 (2025). https://arxiv.org/abs/2504.17148 

A Diffuse Domain Approximation with Transmission-Type Boundary Conditions I: Asymptotic Analysis and Numerics.  (with T. Luong, S. M. Wise, M. H. Wong ). International Journal of Numerical Analysis and Modeling, Vol 22, Num 5, Pages 694-727 (2025). https://arxiv.org/abs/2412.07007 

Asymptotic compatibility of parametrized optimal design problems (with A. Salgado and J. Siktar).  Submitted for publication (2025). https://arxiv.org/abs/2412.04630  

Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes, (with E. Otarola and A. Salgado). Journal of Differential Equations, Vol 412, Pages 250-271, (2024). https://arxiv.org/abs/2406.10762 

Compactness results for a Dirichlet energy of nonlocal gradient with applications, (with Z. Han and X. Tian). Numerical Methods for Partial Differential Equations, Vol 40, Issue 6 (2024). https://arxiv.org/abs/2404.09079 

Calderon-Zygmund theory for strongly coupled linear system of nonlocal equations with Holder-regular coefficient, (with A. Schikorra, A. Seesanea, and S. Yeepo). Advances in Calculus of Variations, Vol 18, Num 2, Pages 421-438 (2025). https://arxiv.org/abs/2401.01886 

Linearization and localization of nonconvex functionals motivated by nonlinear peridynamic models, (With J. Scott). Continuum Mechanics and Thermodynamics, Vol 36, Pages 792-824 (2024). https://arxiv.org/abs/2306.15446 

Fractional Korn’s inequalities without boundary conditions, (with D. Harutyunyan, H. Mikayelyan, and J. M. Scott). Mathematics and Mechanics of Complex Systems. 2023. Vol. 11, No. 4, 497–524 (2023).  https://arxiv.org/abs/2302.14588 

On the Optimal Control of a Linear Peridynamics Model (with A. Salgado and J. Siktar).  Applied Mathematics and Optimization.  Vol 88, No 70 (2023). https://arxiv.org/abs/2304.09328 

Lp-compactness criteria with an application to variational convergence of some nonlocal energy functionals (with Q. Du and X. Tian).  Mathematics in Engineering. Vol 5, issue 6: 1-31 (2023). https://arxiv.org/abs/1801.08000 

Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition (with M. D'Elia, M. Gulian, and J. Scott). Journal Fractional Calculus and Applied Analysis. Vol 25, Pages 2488-2531 (2022).  https://arxiv.org/abs/2112.05317 

Calderon-Zygmund Theory for non-convolution type nonlocal equations with continuous coefficient (with M.M. Fall, A. Schikorra, and S. Yeepo).  Partial Differ. Equ. Appl.3, 24 (2022).  https://arxiv.org/abs/2109.04879 

Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization (with Q. Du and X. Tian). Analysis and Applications. Vol 20, No, 03, pp 579-614 (2022).  https://arxiv.org/abs/2103.09387

Self-improving inequalities for bounded weak solutions to nonlocal double phase equations  (with J. Scott). Communications on Pure and Applied Analysis, 21,1,183-212 (2022). https://arxiv.org/abs/2011.11466  

A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations (with J. Scott). In: Mengesha, T., Salgado, A.J. (eds) A3N2M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models. The IMA Volumes in Mathematics and its Applications, vol 165. Springer. (2023) https://arxiv.org/abs/2011.12779   

A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations (with J. Scott).  Commun.Math. Sci. Vol. 20, N0. 2, 405-423. 2022.  https://arxiv.org/abs/2011.12407 

The Darcy problem with porosity depending exponentially on the pressure (with Z. K. Birhanu and A.J. Salgado).  Journal of Computational and Applied Mathematics, Volume 398, 15 December 2021, 113642. https://arxiv.org/abs/2011.02667

Calderon-Zygmund type estimates for nonlocal PDE with Holder continuous kernel (with A. Schikorra and S. Yeepo), Advances in Mathematics, 383 (2021), 107692.  64 pp. 

Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients (with J. Scott).   SIAM Multiscale Modeling and Simulations.  18 (2020), no. 4, 1462--1488.

The Solvability of a Strongly-Coupled Nonlocal System of Equations, (with J. Scott). Journal of Mathematical Analysis and Applications,  486, 2, 2020.

Weighted-W^{1,p} estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable (with T. Phan).  Nonlinear Analysis, 179, 184-236, 2019.

A fractional Korn-type inequality (with J. Scott). Discrete and Continuous Dynamical Systems,  39(6): 3315--3343 (29 pages), 2019. 

A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics (with J. Scott). SIAM Journal on Mathematical Analysis, 51(1):86-109 (24 pages), 2019 

Solvability of nonlocal systems related to peridynamics (with M. Kassmann and J. Scott).  Communications in Pure and Applied Analyis, 18(3): 1303-1332, 2019. 

Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients (with D. Cao and T. Phan). Proceedings of the AMS Contemporary Mathematics, Volume 725 2019. DOI: https://doi.org/10.1090/conm/725 

Fractional Korn and Hardy-type inequalities for vector fields in half space. Communications in Contemporary Mathematics, Vol. 21, No. 7 (2019). }

Weighted gradient estimates for linear degenerate elliptic equation on Reifenberg flat domains (with D. Cao, and T. Phan).  Indiana University Mathematics Journal, 67(6) 2225-2277, DOI 10.1512/iumj.2018.67.7533, 2018.  

Weighted gradient estimates for linear elliptic equation with discontinuous coefficients (with K. Adimurthi and N. C. Phuc).  Applied Mathematics and Optimization,  83, no. 1, 327–371, 2021. Arxiv

Characterization of function spaces of vector fields and an application in nonlinear peridynamics (with Q. Du).  Nonlinear Analysis and Series A: Theory, Methods & Applications, Volume 140, pp 82--111, 2016.

Quasilinear Riccati type equations with distributional data in Morrey space framework (with N.C. Phuc).  Journal of Differential Equations, 260 pp 5421--5449, 2016. 

Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media (with R. Lipton and Q. Du). ESIAM:Mathematical Modeling and Numerical Analysis, Volume 50, Number 5, pp 1425-1455, 2016. 

On the variational limit of a class of nonlocal functionals related to peridynamics (with Q. Du).  Nonlinearity, Volume 28, Number 11, pp 3999-4035, 2015.

Multiscale Analysis of a linear peridynamic solid (with Q. Du).  Communications in Mathematical Sciences. Volume 13, Number 5, pp 1193-1218, 2015.

Localization of nonlocal gradients in various topologies (with D. Spector).  Calculus of Variations and Partial Differential Equations, Volume 52, Issue 1-2, pp 253--279, 2015. 

Nonlocal constrained value problems for a linear peridynamic Navier equation (with Q. Du).  Journal of Elasticity, Volume 116, pp 27-51, 2014.

The bond-based peridynamic system with Dirichlet-type volume constraint (with Q. Du).  Proc. of the Royal Soc. of Edinburgh: Section A, Volume 144, pp 161--186, 2014. 

Analysis of the peridynamic model with a sign changing kernel (Q. Du).  Discrete and Continuous Dynamical Systems- Series B, Volume 18, Number 5, 1415--1437, 2013.

Nonlocal Korn-type characterization of Sobolev vector fields. Communications in Contemporary Mathematics, Volume  14, Number 04, 2012.

Representations of L^\infty norms for weakly convergent sequences of gradient fields in homogenization (with R. Lipton). ESAIM: Mathematical Modeling and Numerical Analysis, Volume 46, pp1121-1146, 2012.

Global estimates for quasilinear elliptic equations on Reifenberg flat domains (with N.C. Phuc).  Archive for Rational Mechanics and Analysis, Volume 203, Number 1, pp 189-216, 2012.

Weighted and regularity estimates for nonlinear elliptic equations on Reifenberg flat domains (with N. C. Phuc). Journal of Differential Equations, Volume 250, Number 1, pp 1485-2507, 2011.

Results on Nonlocal Boundary Value Problems (with B. Aksoylu). Numerical Functional Analysis and Optimization, Volume 31, Number 12,  pp 1301-1317, 2010.

Sufficient conditions for strong local minima: the case of C^{1} extremals (with Y. Grabovsky). Transactions of the AMS, Volume  361, Number 3, pp 1495-1541, 2009.

Direct approach to the problem of strong local minima in Calculus of Variations (with Y. Grabovsky). Calculus of Variations and PDE, Volume 29, pp 59-83, 2007. Erratum.