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Integral representation of functionals defined on curves of W1,p

Published online by Cambridge University Press:  14 November 2011

Micol Amar ,
Giovanni Bellettini  and
Sergio Venturini
Micol Amar
Affiliation:
Dipartimento di Matematica, Università di Pavia, Via Abbiategrasso 215, 27100 Pavia, Italy, E-mail: amar@dragon.ian.pv.cnr.it
Giovanni Bellettini
Affiliation:
Dipartimento di Matematica Applicata, Università di Pisa, Via Bonanno 25, 56126 Pisa, Italy, E-mail: belletti@dm.unipi.it
Sergio Venturini
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy, E-mail: venturini@dm.unibo.it
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Abstract

Let I ⊂ ℝ be a bounded open interval, (I) be the family of all open subintervals of I and let p > 1. The aim of this paper is to give an integral representation result for abstract functionals F: W1,p(I;ℝn) × (I) → [0, + ∞) which are lower semicontinuous and satisfy suitable properties. In particular, we prove an integral representation theorem for the Г-limit of a sequence {Fh}h, of functionals of the form

where each fh is a Borel function satisfying proper growth conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 193 - 217
Copyright
Copyright © Royal Society of Edinburgh 1998

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