Telephone: (865) 974-6577
Email: mengesha at utk dot edu
Research topics of
interest
- Mathematics
of Materials Science, Calculus of Variations and
Homogenization
Publications and
preprints
- Fractional
Hardy-type and trace theorems for
nonlocal function spaces with heterogeneous localization
(with Q. Du and X.
Tian), Submitted, PDF
- A
Fractional Korn-type inequality for smooth
domains and a regularity estimate for nonlinear nonlocal
systems of equations
(with J. Scott), Submitted, PDF.
- Self-improving
Inequalities for bounded weak
solutions to nonlocal double phase equations (with J.
Scott), Submitted,
PDF.
- The
Darcy problem with porosity depending
exponentially on the pressure, (with Z. K. Birhanu and
A. J. Salgado), Submitted,
PDF.
- Calderon-Zygmund
type estimates for nonlocal PDE with Hφlder
continuous kernel (With A. Schikorra and S. Yeepo), Advances
in
Mathematics 383, 2021,
PDF.
- A
potential space estimate for solutions of systems of
nonlocal equations in
peridynamics (with J. Scott), SIAM Journal of
Mathematical Analysis. 51, no.
1, 86109,
2019, PDF.
- Asymptotic
analysis
of a coupled system of nonlocal equations with
oscillatory
coefficients (with J. Scott), SIAM Multiscale
Modeling and Simulations
18, no. 4, 14621488, 2020, PDF.
- A
fractional Korn-type inequality (with J. Scott), Discrete
Continuous
Dynamical Systems 39, no.
6, 3315-3343, 2019, PDF.
- The
solvability
of a strongly-coupled nonlocal system of equations (with
J. Scott),
Journal of Mathematical Analysis and Applications,
486, no.
2, 2020, PDF.
- 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.
- Fractional
Korn
and Hardy-type inequalities for vector fields in half
space, Communications
in Contemporary Mathematics, 21, no. 7,
2019, PDF.
- Gradient
estimates
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
flows, Contemporary
Mathematics, 725, American Mathematical
Society 2019.
- Weighted-W1,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-W1,p
estimates for weak solutions of degenerate and singular
elliptic equations (with
D. Cao and T. Phan), Indiana University Math
Journal, Vol
67:6, 2018,
PDF.
- Gradient
weighted
norm inequalities for linear elliptic equations
with
discontinuous coefficients (with K. Adimurthi, and
N.C. Phuc), Applied
Mathematics and Optimization, 83, no.
1, 327371, 2021,
PDF.
- Characterization
of
function spaces of vector fields and an application in
nonlinear
peridynamics (with Q. Du), 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), ESAIM:
M2AN
50,
1425-1455 (2016), PDF.
- Localization
of
nonlocal gradients in various topologies (with D.
Spector), Calculus
of Variations and PDEs, 52, 12,
pp 253279, 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,
no. 4, 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,
14951541, 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.