Young measures in a nonlocal phase transition problem

Xiaofeng Ren; Matthias Winter

Young measures in a nonlocal phase transition problem

Xiaofeng Ren
, Matthias Winter

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	615-637
Number of pages	23
Journal	Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Volume	127
Issue number	3
Publication status	Published - 1997

Cite this

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title = "Young measures in a nonlocal phase transition problem",

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.",

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AB - 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.

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M3 - Article

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JF - Proceedings of the Royal Society of Edinburgh, Section A: Mathematics

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Young measures in a nonlocal phase transition problem

Abstract

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