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Lowersemicontinuity of energy clusters

Published online by Cambridge University Press:  14 November 2011

Frank Morgan
Frank Morgan
Affiliation:
Department of Mathematics, Williams College, Williamstown, MA 01267, U.S.A e-mail: Frank.Morgan@williams.edu
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Abstract

We discuss existence and lowersemicontinuity for clusters of materials minimising an energy given by a collection of norms φij on the interfaces between regions Ri and Rj. Following Ambrosio and Braides, we exhibit a problem for which the triangle inequality holds but existence fails, and we state a new sufficient condition for lowersemicontinuity, which may be necessary.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 4 , 1997 , pp. 819 - 822
Copyright
Copyright © Royal Society of Edinburgh 1997

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