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

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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 u∈SBV 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, $\Gamma $-limit 
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     author = {Barroso, Ana Cristina and Matias, Jos\'e},
     title = {On a volume constrained variational problem in {SBV}${^2(\Omega )}$ : part {I}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {223--237},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2002},
     doi = {10.1051/cocv:2002009},
     mrnumber = {1925027},
     zbl = {1047.49016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002009/}
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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, Tome 7 (2002), pp. 223-237. doi: 10.1051/cocv:2002009

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