S. Kholmatov

activity

20142025

most citedBose-Hubbard models with on-site and nearest-neighbor interactions: Exactly solvable case

28 citations · 41 across the 17 of their papers we have counts for

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Showing 2025 · math.APShow all

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math.AP2025

Crystalline elastic flow of polygonal curves: long time behaviour and convergence to stationary solutions

Giovanni Bellettini, Shokhrukh Yu. Kholmatov, Matteo Novaga

Given a planar crystalline anisotropy, we study the crystalline elastic flow of immersed polygonal curves, possibly also unbounded. Assuming that the segments evolve by parallel tr…

math.AP2025

A De Giorgi conjecture on the regularity of minimizers of Cartesian area in 1D

Giovanni Bellettini, Shokhrukh Yu. Kholmatov

We prove a $C^{1, 1}$ -regularity of minimizers of the functional $\int_{I} 1 + ∣ D u ∣^{2} + \int_{I} ∣ u - g ∣ d s, u \in B V (I),$ provided $I \subset R$ is a bounded open inte…