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.
|Number of pages||23|
|Journal||Proceedings of the Royal Society of Edinburgh, Section A: Mathematics|
|Publication status||Published - 1997|