Telephone: (865) 974-6577
Email: mengesha at utk dot edu
Research topics of
of Materials Science, Calculus of Variations and
Hardy-type and trace theorems for
nonlocal function spaces with heterogeneous localization
(with Q. Du and X.
Tian), Submitted, PDF
Fractional Korn-type inequality for smooth
domains and a regularity estimate for nonlinear nonlocal
systems of equations
(with J. Scott), Submitted, PDF.
Inequalities for bounded weak
solutions to nonlocal double phase equations (with J.
Darcy problem with porosity depending
exponentially on the pressure, (with Z. K. Birhanu and
A. J. Salgado), Submitted,
type estimates for nonlocal PDE with Hφlder
continuous kernel (With A. Schikorra and S. Yeepo), Advances
Mathematics 383, 2021,
potential space estimate for solutions of systems of
nonlocal equations in
peridynamics (with J. Scott), SIAM Journal of
Mathematical Analysis. 51, no.
of a coupled system of nonlocal equations with
coefficients (with J. Scott), SIAM Multiscale
Modeling and Simulations
18, no. 4, 14621488, 2020, PDF.
fractional Korn-type inequality (with J. Scott), Discrete
Dynamical Systems 39, no.
6, 3315-3343, 2019, PDF.
of a strongly-coupled nonlocal system of equations (with
Journal of Mathematical Analysis and Applications,
2, 2020, PDF.
nonlocal systems related to peridynamics (with M.
Kassmann and J.
Scott), Communications on Pure & Applied
1303-1332, 2019, PDF.
and Hardy-type inequalities for vector fields in half
in Contemporary Mathematics, 21, no. 7,
for weak solutions of linear elliptic systems with
singular-degenerate coefficients (with D. Cao and T.
Phan), 1333, Proceedings
of the AMS Special
Sessions on Spectral Calculus
and Quasilinear PDEs, PDE analysis on fluid
Mathematics, 725, American Mathematical
estimates for weak solutions of degenerate
elliptic equations with
coefficients degenerate in one variable (with T. Phan),
Analysis, 179, 184-236, 2019. PDF.
estimates for weak solutions of degenerate and singular
elliptic equations (with
D. Cao and T. Phan), Indiana University Math
norm inequalities for linear elliptic equations
discontinuous coefficients (with K. Adimurthi, and
N.C. Phuc), Applied
Mathematics and Optimization, 83, no.
1, 327371, 2021,
function spaces of vector fields and an application in
peridynamics (with Q. Du), Nonlinear Analysis, Vol. 140,
with general structures and divergence data on
domains (with N.C. Phuc), Journal of Differential
variational limit of a class of nonlocal functionals
peridynamics (with Q. Du), Nonlinearity,
28, 3999- 4035, 2015, PDF.
of linear evolution equations with applications to
nonlocal models for
heterogeneous media (with Q. Du, R. Lipton), ESAIM:
1425-1455 (2016), PDF.
nonlocal gradients in various topologies (with D.
of Variations and PDEs, 52, 12,
pp 253279, 2015 PDF.
of a linear peridynamic solid (with Q. Du), Communications
Mathematical Sciences, Vol 13,
No. 15, 1193-1218, 2015, PDF.
system as a nonlocal boundary value problem (with Q.
of Elasticity, 116, 27-51, 2014, PDF.
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.
the peridynamic model for sign changing kernels (with Q.
and Continuous Dynamical Systems- Series B,
18, no 5,
1415-1437, 2013, PDF.
- Nonlocal Korn-type
characterization of Sobolev
vector fields, Communication in Contemporary
no. 4, 2012,
- Global estimates for
equations on Reifenberg flat domains (with N.C. Phuc),
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.
Modelling and Numerical
Analysis, 46, 1121-1146, (2012), PDF.
- Weighted and regularity
nonlinear equations on Reifenberg flat domains (with
N.C. Phuc), Journal
of Differential Equations, 250, 1, 1485-2507, 2011,
- 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,
14951541, 2009, PDF.
- Direct approach to the
problem of strong local
min in Calculus of Variations (with Y. Grabovsy), Calculus
and PDE, 29, No. 1, 59-83,
for local minimizers in Calculus of Variations. Ph.D.