Integral representation of functionals defined on curves of W1,p

Author:

Amar Micol,Bellettini Giovanni,Venturini Sergio

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

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference24 articles.

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4. 15 De Giorgi E. . Teoremi di semicontinuitàa nel calcolo delle variazioni (Notes of a course held at the Istituto Nazionale di Alta Matematica, Roma, 1968–9).

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