It is not hard to write down the Euler-Lagrange equation of a functional, but for a given PDE, how to prove the existence and uniqueness of its energy functional? And for a PDE that has an energy functional, is there a general method to find its energy functional? If not, there must have been some methods to find the energy functionals associated with PDEs of certain types, can anyone please tell me where I can find some references?
2026-03-27 10:10:45.1774606245
How to find the energy functional of a given PDE?
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