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Relaxation of second order geometric integrals and non-local effects


Anza Hafsa, O; Mandallena, J-P (2004). Relaxation of second order geometric integrals and non-local effects. Journal of Nonlinear and Convex Analysis, 5(3):295-306.

Abstract

We are concerned with the relaxation of second-order geometric integrals, i.e., functionals of the type:
C c ∞ (ℝ N )∋u↦F μ (u):=∫ ℝ N f∇ 2 u (x)dμ(x),
where ∇ 2 u is the Hessian of u, f:MsymN→[0,+∞] is a continuous function, and μ is a finite positive Radon measure on ℝ N . A relaxation problem of this type was studied for the first time by G. Bouchitté and I. Fragala , where they pointed out a new phenomenon: the functional relaxed of F μ has, in general, a 'non-local' representation. Working on a more formal level than in, we develop an alternative method making clear this 'strange phenomenon'.

We are concerned with the relaxation of second-order geometric integrals, i.e., functionals of the type:
C c ∞ (ℝ N )∋u↦F μ (u):=∫ ℝ N f∇ 2 u (x)dμ(x),
where ∇ 2 u is the Hessian of u, f:MsymN→[0,+∞] is a continuous function, and μ is a finite positive Radon measure on ℝ N . A relaxation problem of this type was studied for the first time by G. Bouchitté and I. Fragala , where they pointed out a new phenomenon: the functional relaxed of F μ has, in general, a 'non-local' representation. Working on a more formal level than in, we develop an alternative method making clear this 'strange phenomenon'.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Yokohama
ISSN:1345-4773
Official URL:http://www.ybook.co.jp/online/jncae/vol5/num3.htm
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2111605

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