34 citations · 63 across the 31 of their papers we have counts for
29 papers · 1 filter
The -Limit Problem: Convergence of a Linear Degenerate Interface Transmission Problem
Toai Luong, Tadele Mengesha, Kerrek Stinson +2
We study the singular limit of a family of linear degenerate interface transmission problems arising from a regularization procedure in the newly proposed Two-Parameter Diffuse Dom…
Self-improving properties for a class of elliptic and parabolic equations on bounded domains
Tadele Mengesha, Abner J. Salgado
We discuss self improving properties of some local and nonlocal, elliptic and parabolic, equations on bounded domains. We employ a functional analytic approach wherein the solution…
A note on the -solvability of a strongly-coupled nonlocal system of equations
Tadele Mengesha, Miriam Abbate
The goal of this paper is to study the -solvability of the strongly-coupled nonlocal system \[ \mathbb{L} \mathbf{u} (\mathbf{x}) + λ\mathbf{u}(\mathbf{x})= \mathbf{f}(\mathbf…
On parameterized nonlocal-fractional transmission problems and associated function spaces
Qiang Du, Zhaolong Han, Tadele Mengesha +2
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of…
A Diffuse Domain Approximation with Transmission-Type Boundary Conditions II: Gamma--Convergence
Toai Luong, Tadele Mengesha, Steven M. Wise +1
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by rep…
A Diffuse Domain Approximation with Transmission-Type Boundary Conditions I: Asymptotic Analysis and Numerics
Toai Luong, Tadele Mengesha, Steven M. Wise +1
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly repr…
Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes
Tadele Mengesha, Enrique Otarola, Abner J. Salgado
We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is as…
Compactness results for a Dirichlet energy of nonlocal gradient with applications
Zhaolong Han, Tadele Mengesha, Xiaochuan Tian
We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a…
Calderon-Zygmund theory for strongly coupled linear system of nonlocal equations with Holder-regular coefficient
Tadele Mengesha, Armin Schikorra, Adisak Seesanea +1
We extend the Calderón-Zygmund theory for nonlocal equations to strongly coupled system of linear nonlocal equations , where the operator $\mathcal{L}^{s…
Linearization and localization of nonconvex functionals motivated by nonlinear peridynamic models
Tadele Mengesha, James M. Scott
We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal st…
Fractional Korn's inequalities without boundary conditions
D. Harutyunyan, T. Mengesha, H. Mikayelyan +1
This work establishes fractional analogues of Korn's first and second inequalities for vector fields in fractional Sobolev spaces defined over a bounded domain. The validity of the…
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
Marta D'Elia, Mamikon Gulian, Tadele Mengesha +1
Nonlocal vector calculus, which is based on the nonlocal forms of gradient, divergence, and Laplace operators in multiple dimensions, has shown promising applications in fields suc…
Calderon-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient
Mouhamed Moustapha Fall, Tadele Mengesha, Armin Schikorra +1
Given , and , we establish interior Calderon-Zygmund estimates for solutions of nonlocal equations of the form \[ \int_Ω \int_…
Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization
Qiang Du, Tadele Mengesha, Xiaochuan Tian
In this work, we prove some trace theorems for function spaces with a nonlocal character that contain the classical space as a subspace. The result we obtain generalizes…
A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations
James M. Scott, Tadele Mengesha
In this note we prove an estimate on the level sets of a function with growth that depends on the difference quotient of a bounded weak solution to a nonlocal double phase…
A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations
Tadele Mengesha, James M. Scott
In this paper we prove a fractional analogue of the classical Korn's first inequality. The inequality makes it possible to show the equivalence of a function space of vector field…
Self-improving Inequalities for bounded weak solutions to nonlocal double phase equations
James M. Scott, Tadele Mengesha
We prove higher Sobolev regularity for bounded weak solutions to a class of nonlinear nonlocal integro-differential equations. The leading operator exhibits nonuniform growth, swit…
The Darcy problem with porosity depending exponentially on the pressure
Zerihun Kinfe Birhanu, Tadele Mengesha, Abner J. Salgado
We consider the flow of a viscous incompressible fluid through a porous medium. We allow the permeability of the medium to depend exponentially on the pressure and provide an analy…
Calderon-Zygmund type estimates for nonlocal PDE with Hölder continuous kernel
Tadele Mengesha, Armin Schikorra, Sasikarn Yeepo
We study interior -regularity theory, also known as Calderon-Zygmund theory, of the equation \[ \int_{\mathbb{R}^n} \int_{\mathbb{R}^n} \frac{K(x,y)\ (u(x)-u(y))\, (φ(x)-φ(y))…
Asymptotic Analysis of a Coupled System of Nonlocal Equations with Oscillatory Coefficients
Tadele Mengesha, James M. Scott
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by…
The Solvability of a Strongly-Coupled Nonlocal System of Equations
Tadele Mengesha, James M. Scott
We prove existence and uniqueness of strong (pointwise) solutions to a linear nonlocal strongly coupled hyperbolic system of equations posed on all of Euclidean space. The system o…
A fractional Korn-type inequality
James Scott, Tadele Mengesha
We show that a class of spaces of vector fields whose semi-norms involve the magnitude of "directional" difference quotients is in fact equivalent to the class of fractional Sobole…
Gradient weighted norm inequalities for linear elliptic equations with discontinuous coefficients
Karthik Adimurthi, Tadele Mengesha, Nguyen Cong Phuc
Local and global weighted norm estimates involving Muckenhoupt weights are obtained for gradient of solutions to linear elliptic Dirichlet boundary value problems in divergence for…
Solvability of nonlocal systems related to peridynamics
Moritz Kassmann, Tadele Mengesha, James Scott
In this work, we study the Dirichlet problem associated with a strongly coupled system of nonlocal equations. The system of equations comes from a linearization of a model of perid…