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 S0308210500012749_eqnU1 where each fh is a Borel function satisfying proper growth conditions
Amar, M., Bellettini, G., Venturini, S. (1998). Integral representation of functionals defined on curves of W^1,p. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 128(2), 193-217 [10.1017/S0308210500012749].
Integral representation of functionals defined on curves of W^1,p
Bellettini, Giovanni;
1998-01-01
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 S0308210500012749_eqnU1 where each fh is a Borel function satisfying proper growth conditions
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https://hdl.handle.net/11365/1017464