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Pattern evolution. (English) Zbl 0712.49039
A variational model of the evolution of Euclidean sets is proposed. In particular it includes the evolution of sets either of finite perimeter or with boundary of fractional dimension. This model of morphogenesis is based on the introduction of a discontinuous hysteresis effect in time; it consists of a system of two variational inequalities coupled with a nonconvex constraint. The existence of a solution is proven by means of approximation by time discretization, a priori estimates and passage to the limit. Applications to the study of two-phase systems with surface tension, and to pattern interpolation are also discussed.
Reviewer: A.Visintin

MSC:
49Q05 Minimal surfaces and optimization
49J40 Variational inequalities
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