Abstract

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, Série 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].

Author information

Contact details are reproduced from the original publication and may be historical.

Emmanuel Giner

Laboratoire MIP, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France

giner@mip.ups-tlse.fr

Keywords

  • Decomposability
  • richness
  • essential infimum
  • measurable integrand
  • integral functional
  • duality
  • Lagrange multipliers

Mathematics Subject Classification

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

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Suggested citation

E. Giner. “Lagrange Multipliers and Lower Bounds for Integral Functionals.” Journal of Convex Analysis 17 (2010), No. 1, 301–308. https://doi.org/10.68381/jca17022

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Published by Heldermann Verlag, 2010. Rights now held by Banach Press.