Functional Analysis Approach for the Derivation of Hybrid Variational Functionals.
NAPLES UNIV (ITALY) ISTITUTO DI AERODINAMICA
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The original boundary value problems is embedded in a larger class of b.v. problem pertaining to physical quantities of tensorial order higher than that of the original problem. The new b.v. problem is interpreted as defining an isomorphism between two appropriate Hilbert spaces the constraint space and the solution space H, the unique solution of the original b.v. problem being thus characterized as the unique element of H satisfying a prescribed set of constraints. Then variational formulations are deduced by 1 defining subsets of H satisfying an arbitrary number of such constraints thus generalizing the notions of equilibrating and compatible solutions 2 characterizing the solution vector as the unique element common to two such subsets 3 finding the appropriate functional, defined over these two subsets, which is rendered stationary in particular minimum by the exact solution.
- Theoretical Mathematics
- Fluid Mechanics