On a volume constrained variational problem in SBV 2 (Ω) : part I
ESAIM: Control, Optimisation and Calculus of Variations, Volume 7 (2002), pp. 223-237.

We consider the problem of minimizing the energy

E(u):= Ω |u(x)| 2 dx+ S u Ω 1+|[u](x)|dH N-1 (x)
among all functions uSBV 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.

DOI: 10.1051/cocv:2002009
Classification: 49J45,  35R35,  76T05
Keywords: special functions of bounded variation, level sets, lower semicontinuity, Γ-limit
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     author = {Barroso, Ana Cristina and Matias, Jos\'e},
     title = {On a volume constrained variational problem in {SBV}${^2(\Omega )}$ : part {I}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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     publisher = {EDP-Sciences},
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Barroso, Ana Cristina; Matias, José. On a volume constrained variational problem in SBV${^2(\Omega )}$ : part I. ESAIM: Control, Optimisation and Calculus of Variations, Volume 7 (2002), pp. 223-237. doi : 10.1051/cocv:2002009. http://archive.numdam.org/articles/10.1051/cocv:2002009/

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