34 citations · 63 across the 31 of their papers we have counts for
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Asymptotic compatibility of parametrized optimal design problems
Tadele Mengesha, Abner J. Salgado, Joshua M. Siktar
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent,…
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…