S. Kholmatov

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math.AP2026

Existence of minimizers for the SDRI model in $R^{n}$ : Wetting and dewetting regimes with mismatch strain

Shokhrukh Kholmatov, Paolo Piovano

The existence and the regularity results obtained in [37] for the variational model introduced in [36] to study the optimal shape of crystalline materials in the setting of stress-…

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…

Existence of minimizers for the SDRI model in Rn: Wetting and dewetting regimes with mismatch strain

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

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

Existence of minimizers for the SDRI model in $R^{n}$ : Wetting and dewetting regimes with mismatch strain