output
19952025
most citedThree-dimensional coordinates of individual atoms in materials revealed by electron tomography

209 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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12 papers · 1 filter

math.AP2022★ 1 cited

Tetrahedral frame fields via constrained third order symmetric tensors

Dmitry Golovaty, Matthias Kurzke, Jose Alberto Montero +1

Tetrahedral frame fields have applications to certain classes of nematic liquid crystals and frustrated media. We consider the problem of constructing a tetrahedral frame field in…

math.AP2020★ 10 cited

Saturn ring defect around a spherical particle immersed in nematic liquid crystal

Stan Alama, Lia Bronsard, Dmitry Golovaty +1

We consider a nematic liquid crystal occupying the three-dimensional domain in the exterior of a spherical colloid particle. The nematic is subject to Dirichlet boundary conditions…

math.AP2019

A variational singular perturbation problem motivated by Ericksen's model for nematic liquid crystals

Dmitry Golovaty, Itai Shafrir

We study the asymptotic behavior, when , of the minimizers for the energy \begin{equation*} E_\varepsilon(u)=\int_Ω\Big(|\nabla…

math.AP2016★ 29 cited

Dimension reduction for the Landau-de Gennes model on curved nematic thin films

Dmitry Golovaty, Alberto Montero, Peter Sternberg

We use the method of -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of v…

math.AP2015

Interior gradient estimates for quasilinear elliptic equations

Truyen Nguyen, Tuoc Phan

We study quasilinear elliptic equations of the form in bounded domains in , . The vector field…

math.AP2015★ 1 cited

Local gradient estimates for degenerate elliptic equations

Luan Hoang, Truyen Nguyen, Tuoc Phan

This paper is focused on the local interior -regularity for weak solutions of degenerate elliptic equations of the form $\text{div}[\mathbf{a}(x,u, \nabla u)] +b(x, u…

math.AP2013★ 4 cited

Gelfand type problem for two phase porous media

Peter V. Gordon, Vitaly Moroz

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to t…

math.AP2013★ 53 cited

On Minimizers of the Landau-de Gennes Energy Functional on Planar Domains

Dmitry Golovaty, Alberto Montero

We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain with non-contractible boundary data. Here the tensorial field re…

math.AP2013

Effective models for nematic liquid crystals composites with ferromagnetic inclusions

M. Carme Calderer, Antonio DeSimone, Dmitry Golovaty +1

Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is…

math.AP2012★ 10 cited

Geometric properties of boundary sections of solutions to the Monge--Ampère equation and applications

Nam Q. Le, Truyen Nguyen

In this paper, we establish several geometric properties of boundary sections of convex solutions to the Monge-Ampère equations: the engulfing and separating properties and volume…

math.AP2012★ 8 cited

Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source

Peter V. Gordon, Cyrill B. Muratov

This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecul…

math.AP2006★ 2 cited

Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundary

Leonid Berlyand, Dmitry Golovaty, Volodymyr Rybalko

Suppose that . In the annular domain we consider the class of complex valued maps having degree 1 on and on .…