Summary
The paper shows the key place of the choice of the bilinear form in order to give a variational formulation to a given problem. In particular it is shown how the use of a convolution bilinear form makes possible a variational formulation for linear initial value problems.
A critical survey of the three main methods that was devised in the past to solve the same problem is done.
Sunto.
La nota mette in evidenza il ruolo fondamentale della scelta di una forma bilineare al fine di dare formulazione variazionale ad un dato problema. In particolare è mostrato come l'uso di una forma bilineare di convoluzione renda possibile la formulazione variazionale dei problemi ai valori iniziali.
Si fa un esame critico dei tre principali metodi che sono stati escogitati nel passato per risolvere lo stesso problema.
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This work has been sponsored by the Consiglio Nazionale delle Ricerche.
Entrata in Redazione il 19 novembre 1971.
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Tonti, E. On the variational formulation for linear initial value problems. Annali di Matematica 95, 331–359 (1973). https://doi.org/10.1007/BF02410725
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DOI: https://doi.org/10.1007/BF02410725