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Young measures in a nonlocal phase transition problem

Published online by Cambridge University Press:  14 November 2011

Xiaofeng Ren  and
Matthias Winter
Xiaofeng Ren
Affiliation:
Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, U.S.A.
Matthias Winter
Affiliation:
Department of Mathematics, Heriot-Watt University, Edinburgh, U.K.
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Abstract

A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for Young measures and the principle of concentration-compactness. The regularity of such global minimisers is discussed, and the nonlocal variational problem is also considered on asymptotic tubes.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 3 , 1997 , pp. 615 - 637
Copyright
Copyright © Royal Society of Edinburgh 1997

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