Assistant Professor of Mathematics
Telephone: (865) 974-4271
Research topics of
of Materials Science, Calculus of Variations and
estimates for weak solutions of degenerate elliptic
equations with coefficients degenerate in one variable,
(with T. Phan) Submitted, PDF.
estimates for weak solutions of degenerate and singular
elliptic equations, (with D. Cao and T. Phan), To
appear in Indiana University Mathematics Journal, PDF.
weighted norm inequalities for linear elliptic
equations with discontinuous coefficients, (with
K. Adimurthi, and N.C. Phuc). To appear in the
Journal of Differential and Integral Equations, PDF.
of function spaces of vector fields and an application
in nonlinear peridynamics, Nonlinear
Analysis and Series A: Theory, Methods &
Applications, Vol. 140, 82-111, 2016 PDF.
equations with general structures and divergence data on
Reifenberg flat domains (with N.C. Phuc), Journal
of Differential Equations 260, 5421-5449, 2016 PDF.
the variational limit of a class of nonlocal functionals
related to peridynamics (with Q. Du), Nonlinearity,
28, 3999- 4035, 2015 PDF.
analysis of linear evolution equations with applications
to nonlocal models for heterogeneous media (with Q. Du,
R. Lipton), to appear in ESAIM:Mathematical
Modelling and Numerical Analysis, PDF.
of nonlocal gradients in various topologies(with D.
Spector), Calculus of Variations and PDE , 52, 1–2, pp
analysis of a linear peridynamic solid (with Q. Du), Communications
in Mathematical Sciences, Vol 13, No.
15, 1193-1218, 2015 PDF.
peridynamic system as a nonlocal boundary value problem
(with Q. Du),
Journal of Elasticity, 116,
27-51, 2014, PDF.
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
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),
- Representation formulas for
L-infinity norms of weakly convergent sequences of
gradient fields in homogenization, (with R. Lipton),
Modelling and Numerical Analysis, 46 1121-1146, (2012),
- 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.
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