Telephone: (865) 974-6577
Email: mengesha at utk dot edu
Research topics of
of Materials Science, Calculus of Variations and
- 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 18, 3,
1303-1332, 2019. PDF.
- 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, To
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), To
appear in the Proceedings of the AMS Contemporary
estimates for weak solutions of degenerate elliptic
equations with coefficients degenerate in one variable,
(with T. Phan), Nonlinear Analysis, 179, 184-236,
estimates for weak solutions of degenerate and singular
elliptic equations, (with D. Cao and T. Phan),
Indiana Univ Math Journal Vol
weighted norm inequalities for linear elliptic
equations with discontinuous coefficients, (with
K. Adimurthi, and N.C. Phuc). To appear
in Applied Mathematics and
of function spaces of vector fields and an application
in nonlinear peridynamics, Nonlinear Analysis
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), ESAIM:M2AN50
(2016) 1425-1455, 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