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Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation
Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto
This survey hinges on the interplay between regularity and approximation for linear and quasi-linear fractional elliptic problems on Lipschitz domains. For the linear Dirichlet int…
Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation
Lucas Bouck, Ricardo H. Nochetto, Shuo Yang
We examine a reduced membrane model of liquid crystal polymer networks (LCNs) via asymptotics and computation. This model requires solving a minimization problem for a non-convex s…
Convergent FEM for a membrane model of liquid crystal polymer networks
Lucas Bouck, Ricardo H. Nochetto, Shuo Yang
We design a finite element method (FEM) for a membrane model of liquid crystal polymer networks (LCNs). This model consists of a minimization problem of a non-convex stretching ene…
A hydrodynamical model of nematic liquid crystal films with a general state of orientational order
Lucas Bouck, Ricardo H. Nochetto, Vladimir Yushutin
We develop a Q-tensor model of nematic liquid crystals occupying a stationary surface which represents a fluidic material film in space. In addition to the evolution due to Landau-…