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Journal of Convex Analysis 17 (2010), No. 1, 301--308
Copyright Heldermann Verlag 2010



Lagrange Mulitpliers and Lower Bounds for Integral Functionals

Emmanuel Giner
Laboratoire MIP, UniversitÚ Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
giner@mip.ups-tlse.fr



We present a large class of examples with the remarkable property pointed out by B. Ricceri in "A variational property of integral functionals on Lp spaces of vector-valued functions" [C. R. Acad. Sci. Paris, SÚrie I Math. 318 (1994) 337--342], "More on a variational property of integral functionals" [J. Optimisation Theory Appl. 94 (1997) 757--763], and in "Further considerations on a variational property of integral functionals" [J. Optimisation Theory Appl. 106 (2000) 677--681], about lower bounds of integral functionals. We use only a Lagrange duality result of A. Bourass and E. Giner [see: "Kuhn-Tucker conditions and integral functionals", J. Convex Analysis 8 (2001) 533--553].

Keywords: Decomposability, richness, essential infimum, measurable integrand, integral functional, duality, Lagrange multipliers.

MSC: 26A51, 26B20, 26E15, 28B15; 28B20, 46E30, 46N10, 49K40

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