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

Ana Cristina Barroso; José Matias

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 7, page 223-237
- ISSN: 1292-8119

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topBarroso, Ana Cristina, and Matias, José. "On a Volume Constrained Variational Problem in SBV²(Ω): Part I." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 223-237. <http://eudml.org/doc/90619>.

@article{Barroso2010,

abstract = {
We consider the problem of minimizing the energy
$$ E(u):= \int\_\{\Omega\}|\nabla u(x)|^2 \, \{\rm d\}x + \int\_\{S\_u \cap \Omega\}\left
(1 + |[u](x)|\right) \, \{\rm d\}H^\{N - 1\}(x)$$
among all functions u ∈ SBV²(Ω) for which two level sets $\\{u = l_i\\}$
have prescribed Lebesgue measure $\alpha_i$. Subject to this volume constraint
the existence of minimizers for E(.) is proved and the asymptotic
behaviour of the solutions is investigated.
},

author = {Barroso, Ana Cristina, Matias, José},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Special functions of bounded variation; level sets;
lower semicontinuity; Γ-limit.; special functions of bounded variation; lower semicontinuity; -limit; SBV},

language = {eng},

month = {3},

pages = {223-237},

publisher = {EDP Sciences},

title = {On a Volume Constrained Variational Problem in SBV²(Ω): Part I},

url = {http://eudml.org/doc/90619},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Barroso, Ana Cristina

AU - Matias, José

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 223

EP - 237

AB -
We consider the problem of minimizing the energy
$$ E(u):= \int_{\Omega}|\nabla u(x)|^2 \, {\rm d}x + \int_{S_u \cap \Omega}\left
(1 + |[u](x)|\right) \, {\rm d}H^{N - 1}(x)$$
among all functions u ∈ SBV²(Ω) for which two level sets $\{u = l_i\}$
have prescribed Lebesgue measure $\alpha_i$. Subject to this volume constraint
the existence of minimizers for E(.) is proved and the asymptotic
behaviour of the solutions is investigated.

LA - eng

KW - Special functions of bounded variation; level sets;
lower semicontinuity; Γ-limit.; special functions of bounded variation; lower semicontinuity; -limit; SBV

UR - http://eudml.org/doc/90619

ER -

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