Given a critical point of a C(2)-functional on a separable Hilbert space, we obtain sufficient conditions for it to be detectable (i.e. 'visible') from finite-dimensional Rayleigh-Ritz- Galerkin (RRG) approximations. While examples show that even nondegenerate critical points are, without any further restriction, not visible, we single out relevant classes of smooth functionals, e.g. the Hamiltonian action on the loop space or the functionals associated with boundary value problems for somes emilinear elliptic equations, such that their nondegenerate critical points are visible from their RRG approximations. (C) 2010 Elsevier Ltd. All rights reserved.

Detectability of critical points of smooth functionals from their finite-dimensional approximations / F. Sani, M. Villarini. - In: NONLINEAR ANALYSIS. B, REAL WORLD APPLICATIONS. - ISSN 1878-5719. - 73:9(2010), pp. 3140-3150. [10.1016/j.na.2010.06.086]

Detectability of critical points of smooth functionals from their finite-dimensional approximations

F. Sani;
2010

Abstract

Given a critical point of a C(2)-functional on a separable Hilbert space, we obtain sufficient conditions for it to be detectable (i.e. 'visible') from finite-dimensional Rayleigh-Ritz- Galerkin (RRG) approximations. While examples show that even nondegenerate critical points are, without any further restriction, not visible, we single out relevant classes of smooth functionals, e.g. the Hamiltonian action on the loop space or the functionals associated with boundary value problems for somes emilinear elliptic equations, such that their nondegenerate critical points are visible from their RRG approximations. (C) 2010 Elsevier Ltd. All rights reserved.
Rayleigh-Ritz-Galerkin approximations; Approximations of critical points; Hamiltonian systems
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/251088
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