Variational Principles for Problems with Linear Constraints. Prescribed Jumps and Continuation Type Restrictions.

摘要

A general theory of the problems subjected to linear constraints is developed. As applications, a problem for which the solutions are required to satisfy prescribed jumps and another one whose solutions are restricted to be such that they can be continued smoothly into solutions of given equations in neighboring regions, are formulated abstractly. General variational principles for these types of problem are reported. In addition it is shown that sets of functions that can be extended in the manner explained above constitute, generally, completely regular subspaces, here defined. These results have a bearing on boundary methods which are being developed for treating numerically partial differential equations associated with many problems of Science and Engineering. (Author)