9 citations · 9 across the 1 of their papers we have counts for
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A nonlocal isoperimetric problem with density perimeter
Stan Alama, Lia Bronsard, Ihsan Topaloglu +1
We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent , under volume constraint, wh…
Minimality of polytopes in a nonlocal anisotropic isoperimetric problem
Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu
We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in…
On minimizers of an anisotropic liquid drop model
Oleksandr Misiats, Ihsan Topaloglu
We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes ar…
Singular perturbation of an elastic energy with a singular weight
Oleksandr Misiats, Ihsan Topaloglu, Daniel Vasiliu
We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scal…
Anisotropic liquid drop models
Rustum Choksi, Robin Neumayer, Ihsan Topaloglu
We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are est…
Aggregation-Diffusion to Constrained Interaction: Minimizers & Gradient Flows in the Slow Diffusion Limit
Katy Craig, Ihsan Topaloglu
Inspired by recent work on minimizers and gradient flows of constrained interaction energies, we prove that these energies arise as the slow diffusion limit of well-known aggregati…