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Removable singularities of fully nonlinear elliptic equations

In this paper we consider fully nonlinear elliptic equations of the form

F(Du, D²u) =ψ(x,u,Du) ,

including the Monge–Ampère, the Hessian and the Weingarten equations and give conditions which ensure that a singular set E of a solution u is removable...

Keywords: PDE, nonlinear, elliptic, Monge-Ampère, Hessian

01/2007 | Analysis, Oldenbourg Wissenschaftsverlag

On the numerical solution of a semilinear elliptic eigenproblem of LaneEmden type, I: Problem formulation and description of the algorithms

In this first part of our two-part article, we present some theoretical background along with descriptions of some numerical techniques for solving a particular semilinear elliptic eigenproblem of Lane-Emden type on a triangular domain without any lines of symmetry...

Keywords: numerical method, Lane, Emden, semilinear, elliptic, eigenproblem, operator splitting, finite element, arclength continuation, least-squares, control

10/2007 | Journal of Numerical Mathematics, Walter de Gruyter

On the numerical solution of a semilinear elliptic eigenproblem of LaneEmden type, II: Numerical experiments

In this second part of our two-part article, we present and discuss the corresponding numerical results from implementations of the numerical algorithms described in the first part...