From the 1 of 7 linked papers with an AI index.
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Self-improving properties for a class of elliptic and parabolic equations on bounded domains
Tadele Mengesha, Abner J. Salgado
The paper studies how solutions to certain local and nonlocal elliptic and parabolic equations on bounded domains gain extra regularity, using interpolation theory and analytic per…
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}(\mathb…
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…