Duality, Conjugate Functionals, Monotone Operators and Elliptic Differential Equations

Eberhard Zeidler
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Eberhard Zeidler: Sektion Mathematik

Chapter Chapter 51 in Nonlinear Functional Analysis and its Applications, 1985, pp 487-511 from Springer

Abstract: Abstract In Chapter 49 we showed how one arrives at general duality propositions knowing a Lagrange function L. In this chapter, given a functional F, we define a so-called conjugate functional F*, and in Section 51.4 we explain how one can construct a Lagrange function for a given convex minimum problem with respect to F by means of F*. In this connection, the generalized Young inequality 1a F * ( u * ) + F ( u ) ≥ 〈 u * , u 〉 , ]] F * ( u * ) + F ( u ) = 〈 u * , u 〉 ⇔ u * ∈ ∂ F ( u ) ]] F * * = F ]] ( F * ) ′ = ( F ′ ) − 1 ]]

Date: 1985
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DOI: 10.1007/978-1-4612-5020-3_16

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