Theory of connectivity for formally symmetric operators
- 1 November 1977
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 74 (11) , 4722-4725
- https://doi.org/10.1073/pnas.74.11.4722
Abstract
A previous paper introduced the notion of complete connectivity conditions and developed variational principles for diffraction problems subjected to such restrictions. Here, an abstract definition of formally symmetric operators is given and it is shown that the problem of connecting solutions of equations associated with this kind of operators leads to complete connectivity conditions. The variational principles previously developed as well as a present more general one are thus applicable. The problem of connecting solutions defined in different regions is basic for finite element formulations. Formally symmetric operators occur in many branches of science and engineering. Applications are given here to potential theory, wave propagation, elasticity, and a general class of boundary integral equations.Keywords
This publication has 1 reference indexed in Scilit:
- General variational principles applicable to the hybrid element methodProceedings of the National Academy of Sciences, 1977