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Summary: A GENERAL CLASS OF PHASE TRANSITION MODELS
WITH WEIGHTED INTERFACE ENERGY
E. ACERBI, G. BOUCHITT“E
Abstract. We study a family of singular perturbation problems of the kind
inf
1
f(u, u, ) dx :
u = m0 ,
= m1 ,
where u represents a fluid density and the nonnegative energy density f van-
ishes only for u = or u = . The novelty of the model is the additional
variable 0 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 0 and find for each f a transition energy (well defined
when u BV (; {, }) and is a measure) which depends on the n - 1 di-
mensional density of the measure on the jump set of u. An explicit formula
is also given.
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