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On a volume constrained variational problem in SBV 2 ( Ω ) : part I

Ana Cristina BarrosoJosé Matias — 2002

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing the energy E ( u ) : = Ω | u ( x ) | 2 d x + S u Ω 1 + | [ u ] ( x ) | d H N - 1 ( x ) among all functions u S B V 2 ( Ω ) for which two level sets { u = l i } have prescribed Lebesgue measure α i . Subject to this volume constraint the existence of minimizers for E ( · ) is proved and the asymptotic behaviour of the solutions is investigated.

On a Volume Constrained Variational Problem in SBV²(Ω): Part I

Ana Cristina BarrosoJosé Matias — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing the energy E ( u ) : = Ω | u ( x ) | 2 d x + S u Ω 1 + | [ u ] ( x ) | d H N - 1 ( x ) among all functions ∈ ²(Ω) for which two level sets { u = l i } have prescribed Lebesgue measure α i . Subject to this volume constraint the existence of minimizers for (.) is proved and the asymptotic behaviour of the solutions is investigated.

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