Abstract
In many variational problems one must find critical points of a given functional ϕ ∈ C1(X, ℝ) in the presence of constraints, that is, critical points of ϕ restricted to a set M ⊂ X of constraints. Naturally, in order to be able to talk about critical points of ϕ|M, the set M must have a differentiable structure. Typically, in the case of a finite number of constraints, M is of the form M = {u ∈ X | Ψ (u) = 0, j = 1,..., k} where Ψj ∈ C1(X, ℝ), j = 1,...,k.
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© 2007 Birkhäuser Boston
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Costa, D.G. (2007). Critical Points under Constraints. In: An Invitation to Variational Methods in Differential Equations. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4536-6_6
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DOI: https://doi.org/10.1007/978-0-8176-4536-6_6
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4535-9
Online ISBN: 978-0-8176-4536-6
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