TY - JOUR AU - Opara, Uchechukwu Michael AU - Arunaye, Festus Irimisose AU - Ojarikre, Henrietta Ify AU - Mate, Philip Olugbenga PY - 2025 TI - On the Variational Symmetries of P.D.E's Incorporating Boundary Value Constraints JF - Journal of Mathematics and Statistics VL - 21 IS - 1 DO - 10.3844/jmssp.2025.1.7 UR - https://thescipub.com/abstract/jmssp.2025.1.7 AB - A crucial interface between Optimization theory, Trace theory, and Lie Symmetry theory is brought to the fore in this paper, as an enhancement of standard known results established in Partial Differential Equation (P.D.E) analysis. In particular, the incorporation of compatible Boundary Value constraints in the re-assessment of admitted variational symmetries is a key process in the development of the discussions and results. Classical variational formulation techniques for a few Boundary Value Problems are considered. Ramifications of standard and modified admitted variational symmetries in simplification of PDEs constitute further relevant crucial details addressed appreciably.