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On lower semicontinuity and relaxation

Published online by Cambridge University Press:  12 July 2007

Irene Fonseca  and
Giovanni Leoni
Irene Fonseca
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Giovanni Leoni
Affiliation:
Dipartimento di Scienze e Tecnologie Avanzate, Universitá del Piemonte Orientale, Alessandria, Italy 15100
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Abstract

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Lower semicontinuity and relaxation results in BV are obtained for multiple integrals where the energy density f satisfies lower semicontinuity conditions with respect to (x, u) and is not subjected to coercivity hypotheses. These results call for methods recently developed in the calculus of variations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 3 , June 2001 , pp. 519 - 565
Copyright
Copyright © Royal Society of Edinburgh 2001