Research topics of
interest

- Mathematics
of Materials Science, Calculus of Variations and
Homogenization

- A potential space estimate
for solutions of systems of nonlocal equations in
peridynamics (with J. Scott),
**Submitted**

- Solvability of nonlocal systems related to peridynamics,
(with M. Kassmann and J. Scott),
**Communications on Pure & Applied Analysis, Vol**, 2019. PDF.**18, 3, 1303-1332**

- Nonlocal criteria for compactness in the
space of Lp vector fields, (with Q. Du and X. Tian),
Submitted, 2018, PDF.

- Fractional Korn and Hardy-type
inequalities for vector fields in half space,
**T**, 2018, PDF.**o appear in Communications in Contemporary Mathematics**

- Gradient estimates for weak solutions of
linear elliptic systems with singular-degenerate
coefficients, (with D. Cao and T. Phan),
**T**, 2018.**o appear in the Proceedings of the AMS Contemporary Mathematics**

- 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. PDF**

- Weighted-W
^{1,p}estimates for weak solutions of degenerate and singular elliptic equations, (with D. Cao and T. Phan)**,****Indiana Univ Math Journal Vol 67:6****,****PDF.**

- Gradient
weighted norm inequalities for linear elliptic
equations with discontinuous coefficients, (with
K. Adimurthi, and N.C. Phuc).
**To****appear in****Applied Mathematics and Optimization****,****PDF****.**

- Characterization
of function spaces of vector fields and an application
in nonlinear peridynamics,
**Nonlinear Analysis Vol. 140, 82-111, 2016****PDF.**

- Quasilinear
equations with general structures and divergence data on
Reifenberg flat domains (with N.C. Phuc),
**Journal of Differential Equations 260, 5421-5449, 2016 PDF.**

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

- Multiscale
analysis of linear evolution equations with applications
to nonlocal models for heterogeneous media (with Q. Du,
R. Lipton),

- Localization
of nonlocal gradients in various topologies(with D.
Spector),
*Calculus of Variations and P**DE***,****52, 1–2, pp 253–279, 2015**PDF.

- Multiscale
analysis of a linear peridynamic solid (with Q. Du),
,*Communications in Mathematical Sciences***Vol 13, No. 15, 1193-1218, 2015 PDF.**

- The
peridynamic system as a nonlocal boundary value problem
(with Q. Du),
**Journal of Elasticity,****116, 27-51, 2014****, PDF.**

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

- Analysis
of the peridynamic model for sign changing kernels (with
Q. Du),
**Discrete and****Continuous Dynamical Systems- Series B**,**Vol 18, no 5, 1415-1437**,**2013**, PDF.

- Nonlocal Korn-type
characterization of Sobolev vector fields, Communication
in Contemporary Mathematics, 14 (2012),
**PDF**.

- Global estimates for
quasilinear elliptic equations on Reifenberg flat
domains (with N.C.Phuc)
**,**Archive for Rational Mechanics and Analysis, Vol 203, no 1, 189 - 216,(2012),**PDF**.

- Representation formulas for L-infinity norms of weakly convergent sequences of gradient fields in homogenization, (with R. Lipton), ESAIM:Mathematical Modelling and Numerical Analysis, 46 1121-1146, (2012), PDF.

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

- Results on Nonlocal Boundary
value problems, (with B. Aksoylu), Numerical
Functional Analysis and Optimization, 31, 12,
1301-1317, 2010, PDF.

- Sufficient
conditions for strong local minima: the case of C^1
extremals, (with Y. Grabovsky),
*Transactions of the AMS.***361**, No. 3, 1495–1541, 2009, PDF.

- Direct approach
to the problem of strong local min in Calculus of
Variations., (with Y. Grabovsy),
*Calculus of Variations and PDE*,**29**, No. 1, 59-83, 2007, PDF.

- Sufficient Conditions for local minimizers in Calculus of Variations. Ph.D. thesis, 2007. Temple University.