A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur’s com- plement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.

Finite reduction and Morse index estimates for mechanical systems

CARDIN, FRANCO;DE MARCO, GIUSEPPE;SFONDRINI A.
2011

Abstract

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur’s com- plement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/139659
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