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Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

Ayman Kachmar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.

Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators

Dario Daniele Monticelli (2010)

Journal of the European Mathematical Society

We deal with maximum principles for a class of linear, degenerate elliptic differential operators of the second order. In particular the Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypothesis on the degeneracy set of the operator. We derive, as consequences of these principles, some generalized maximum principles and an a priori estimate on the solutions of the Dirichlet problem for the linear equation....

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H 1 norm are derived.

Mimetic finite differences for elliptic problems

Franco Brezzi, Annalisa Buffa, Konstantin Lipnikov (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H1 norm are derived.

Minimal Graphs in ℍ n × ℝ and ℝ n + 1

Ricardo Sà Earp, Eric Toubiana (2010)

Annales de l’institut Fourier

We construct geometric barriers for minimal graphs in ℍ n × ℝ . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in ℍ n extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces.In ℍ n × ℝ , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω ⊂ ℍ n taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...

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