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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.
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....
In this paper we consider the Neumann problem involving a critical Sobolev exponent. We investigate a combined effect of the coefficient of the critical Sobolev nonlinearity and the mean curvature on the existence and nonexistence of solutions.
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 norm are derived.
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.
We construct geometric barriers for minimal graphs in We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in 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 , we solve the Dirichlet problem for the vertical minimal equation in a convex domain taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...
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