28 citations · 41 across the 17 of their papers we have counts for
12 papers · 1 filter
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…
A De Giorgi conjecture on the regularity of minimizers of Cartesian area in 1D
Giovanni Bellettini, Shokhrukh Yu. Kholmatov
We prove a -regularity of minimizers of the functional provided is a bounded open inte…
Minimizing movements for the generalized power mean curvature flow
Giovanni Bellettini, Shokhrukh Yu. Kholmatov
Motivated by a conjecture of De Giorgi, we consider the Almgren-Taylor-Wang scheme for mean curvature flow, where the volume penalization is replaced by a term of the form \[ \int_…
Minimizing movements for forced anisotropic curvature flow of droplets
Shokhrukh Yu. Kholmatov
We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existe…
On the minimality of the Winterbottom shape
Shokhrukh Yu. Kholmatov
In this short note we prove that the Winterbottom shape [Winterbottom: Acta Metallurgica (1967)] is a volume-constraint minimizer of the corresponding anisotropic capillary functio…
Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions
Giovanni Bellettini, Shokhrukh Kholmatov, Firdavsjon Almuratov
We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of…
Existence of minimizers for the SDRI model in : 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-…
Existence of minimizers for the SDRI model in 2d: wetting and dewetting regime with mismatch strain
Shokhrukh Yu. Kholmatov, Paolo Piovano
The model introduced in [Kholmatov-Piovano 2020] in the framework of the theory on Stress-Driven Rearrangement Instabilities (SDRI) [Asaro-Tiller 1972; Grinfeld 1993} for the morph…
Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities
Giovanni Bellettini, Antonin Chambolle, Shokhrukh Yu. Kholmatov
Under suitable assumptions on the family of anisotropies, we prove the existence of a weak global -Hölder continuous in time mean curvature flow with mobilities of a…
A unified model for stress-driven rearrangement instabilities
Shokhrukh Yu. Kholmatov, Paolo Piovano
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wet…
Minimizing movements for mean curvature flow of partitions
Giovanni Bellettini, Shokhrukh Yusufovich Kholmatov
We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case whe…
Minimizers of anisotropic perimeters with cylindrical norms
G. Bellettini, M. Novaga, Sh. Yu. Kholmatov
We study various regularity properties of minimizers of the --perimeter, where is a norm. Under suitable assumptions on and on the dimension of the ambient space, we pro…