B. Tsang, S. W. Taylor, G. C. Wake, "Variational methods for boundary value problems", Advances in Decision Sciences, vol. 4, Article ID 841395, 12 pages, 2000. https://doi.org/10.1155/S1173912600000158
Variational methods for boundary value problems
The variational formulation of boundary value problems is valuable in providing remarkably easy computational algorithms as well as an alternative framework with which to prove existence results. Boundary conditions impose constraints which can be annoying from a computational point of view. The question is then posed: what is the most general boundary value problem which can be posed in variational form with the boundary conditions appearing naturally? Special cases of two-point problems in one-dimension and some higher dimensional problems are addressed. There is a deep connection with self-adjointness for the linear case. Further cases under which a Lagrangian may or may not exist are explained.
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