Normal Operators and Uniformly Elliptic Self-Adjoint Partial Differential Equations

On a Comparison Theorem for Self-adjoint Partial Differential Equations of Elliptic Type

Adaptive computation of smallest eigenvalues of self-adjoint elliptic partial differential equations

We consider a new adaptive finite element (AFEM) algorithm for self-adjoint elliptic PDE eigenvalue problems. In contrast to other approaches we incorporate the inexact solutions of the resulting finite dimensional algebraic eigenvalue problems into the adaptation process. In this way we can balance the costs of the adaptive refinement of the mesh with the costs for the iterative eigenvalue met...

Non-self-adjoint Differential Operators

We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...

Self-adjoint differential-algebraic equations

Adjoint and self - adjoint differential operators on graphs ∗

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...