1-type and biharmonic curves by using laplace operator in lorentzian 3-space arestudied and some theorems and characterizations are given for these curves.

We introduce a new mixed method for the biharmonic problem. The method is based on a formulation where the biharmonic problem is re-written as a system of four first-order equations. A hybrid form of the method is introduced which allows to reduce the globally coupled degrees of freedom to only those associated with Lagrange multipliers which approximate the solution and its derivative at the f...

In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil, no special formulas are needed near th...

This paper is concerned with eigenvalues of the biharmonic operators and the buckling eigenvalue for complete Riemannian manifolds. We are mostly concerned with relating bounds for these eigenvalues to the behavior of the ends of the manifold. Let M be a complete Riemannian manifold. M is called parabolic if every non-positive subharmonic function on M reduces to a constant. By an end E of M we...

In the present paper we establish the Wiener test for boundary regularity of the solutions to the polyharmonic operator. We introduce a new notion of polyharmonic capacity and demonstrate necessary and sufficient conditions on the capacity of the domain responsible for the regularity of a polyharmonic function near a boundary point. In the case of the Laplacian the test for regularity of a boun...

Regular convergence, together with other types of have been studied since the 1970s for discrete approximations linear operators. In this paper, we consider eigenvalue approximation a compact operator $T$ that can be written as an problem holomorphic Fredholm function $F(\eta) = T-\frac{1}{\eta} I$. Focusing on finite element methods (conforming, discontinuous Galerkin, non-conforming, etc.), s...