Intrinsic Self Adjointness and the Calculus of Variations

摘要

In the present paper, an attempt is made for generalizing the calculus of variations in such a way that the end points are left without being constrained, with the purpose of generating Sturm-Liouville differential operators and the like, that are intrinsically self-adjoint. This approach is not only different from the hermitization prescription, but also more superior in view of the fact that self-adjointness is built in naturally. The proposed generalization of the variational calculus provides an Euler-Lagrange differential equation with a differential boundary term, that is responsible for restoring self-adjointness. In this frame, functionals containing higher order derivatives, and multi-dimensional dependent as well as independent variables which may or may not be subjected to some integral constraints are extremized. As a typical example, the Sturm-Liouville problem is considered, in which intrinsic self adjointness is incorporated. 8 references. (ERA citation 12:029763)