Critical Points under Constraints

David G. Costa
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David G. Costa: University of Nevada, Las Vegas, Department of Mathematical Sciences

Chapter 6 in An Invitation to Variational Methods in Differential Equations, 2007, pp 49-62 from Springer

Abstract: 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.

Keywords: Weak Solution; Closed Subspace; Bounded Smooth Domain; Natural Constraint; Differentiable Structure (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-0-8176-4536-6_6

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