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The interaction between bulk energy and surface energy in multiple integrals

Published online by Cambridge University Press:  14 November 2011

Andrea Braides  and
Alessandra Coscia
Andrea Braides
Affiliation:
S.I.S.S.A., via Beirut 2/4,1-34014 Trieste, Italy
Alessandra Coscia
Affiliation:
S.I.S.S.A., via Beirut 2/4,1-34014 Trieste, Italy
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Abstract

This paper is devoted to the study of integral functional denned on the space SBV(Ω ℝk) of vector-valued special functions with bounded variation on the open set Ω⊂ℝn, of the form

We suppose only that f is finite at one point, and that g is positively 1-homogeneous and locally bounded on the sets ℝk⊗vm, where {v1,…, vR} ⊂ Sn−1 is a basis of ℝn. We prove that the lower semicontinuous envelope of F in the L1(Ω;ℝk)-topology is finite and with linear growth on the whole BV(Ω;ℝk), and that it admits the integral representation

A formula for ϕ is given, which takes into account the interaction between the bulk energy density f and the surface energy density g.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 4 , 1994 , pp. 737 - 756
Copyright
Copyright © Royal Society of Edinburgh 1994

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