We study a family of singular perturbation problems of the kind
where u represents a fluid density and the non-negative energy density f vanishes only for or . The novelty of the model is the additional variable which is also unknown and interplays with the gradient of u in the formation of interfaces. Under mild assumptions on f, we characterize the limit energy as and find for each f a transition energy (well defined when and ρ is a measure) which depends on the dimensional density of the measure ρ on the jump set of u. An explicit formula is also given.
Cite this article
E. Acerbi, G. Bouchitté, A general class of phase transition models with weighted interface energy. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 6, pp. 1111–1143DOI 10.1016/J.ANIHPC.2007.09.004