Research topics of
interest
- Nonlocal models and
applications to mechanics (Peridynamics)
- Analysis of Partial Differential
Equations
- Mathematics
of Materials Science, Calculus of Variations and Homogenization
Publications and preprints
- The peridynamic system as a nonlocal boundary value
problem (with Q. Du),
in preparation.
- Quasilinear equations with general structures and
divergence data on Reifenberg flat domains (with N.C. Phuc),
in preparation.
- The bond based peridynamic system with Dirichlet-type
volume constraint (with Q. Du), Proceedings of the Royal
Society of Edinburgh: Section A, accepted,
2012.
- Analysis of the peridynamic model for sign changing
kernels (with Q. Du), Discrete
and Continuous Dynamical Systems- Series B,
accepted, 2012.
- 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)
PDF, 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) PDF, ESAIM:Mathematical
Modelling and Numerical Analysis, 46 1121-1146,
(2012).
- Weighted and regularity
estimates for nonlinear equations on Reifenberg flat domains,
(with N.C. Phuc) PDF,
Journal
of Differential Equations 250, 1, 1485-2507, 2011.
- Results on Nonlocal Boundary
value problems, (with B. Aksoylu) PDF, Numerical
Functional Analysis and Optimization, 31, 12, 1301-1317,
2010.
- Sufficient
conditions for strong local minima: the case of C^1
extremals, (with Y. Grabovsky) PDF,
Transactions of the AMS. 361, No. 3,
1495–1541, 2009.
- Direct approach
to the problem of strong local min in Calculus of
Variations., (with Y. Grabovsy)
PDF, Calculus of
Variations and PDE, 29, No. 1, 59-83, 2007.
- Sufficient Conditions for local minimizers in
Calculus of Variations. Ph.D. thesis, 2007. Temple University.