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Games for eigenvalues of the hessian and concave/convex envelopes
(Elsevier Masson, 2019-07)
We study the PDE λj (D2u) = 0, in Ω, with u = g, on ∂Ω. Here λ1(D2u) ≤ ... ≤ λN (D2u) are the ordered eigenvalues of the Hessian D2u. First, we show a geometric interpretation of the viscosity solutions to the problem in ...
A mathematical basis for the graphene
(2020)
We present a new basis of representation for the graphene honeycomb structure that facilitates the solution of the eigenvalue problem by reducing it to one dimension. We define spaces in these geometrical basis that allow ...
On the graphene Hamiltonian operator
(2020)
We solve a second-order elliptic equation with quasi-periodic boundary conditions defined on a honeycomb lattice that represents the arrangement of carbon atoms in graphene. Our results generalize those found by Kuchment ...
A novel approach to suppress the DC modes in eigenvalue problems using the finite element method
(Wiley-blackwellHobokenEUA, 2013)
Minimization of the first eigenvalue in problems involving the bi-laplacianMinimization of the first eigenvalue in problems involving the bi-laplacian
(2009-02-27)
This paper concerns the minimization of the first eigenvalue in problems involvingthe bi-Laplacian under either homogeneous Navier boundary conditions or homogeneousDirichlet boundary conditions. Physically, in case of N ...
Minimization of the first eigenvalue in problems involving the bi-laplacianMinimization of the first eigenvalue in problems involving the bi-laplacian
(2009-02-27)
This paper concerns the minimization of the first eigenvalue in problems involvingthe bi-Laplacian under either homogeneous Navier boundary conditions or homogeneousDirichlet boundary conditions. Physically, in case of N ...