On a volume constrained variational problem in SBV${^2(\Omega )}$ : part I

Barroso, Ana Cristina; Matias, José

doi:10.1051/cocv:2002009

Geodesic

Parcourir par

On a volume constrained variational problem in SBV

^{2} (Ω)

: part I

Barroso, Ana Cristina ; Matias, José

ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 223-237

Voir la notice de l'article provenant de la source Numdam

Résumé

We consider the problem of minimizing the energy

E (u) : = \int_{Ω} {| \nabla u (x) |}^{2} d x + \int_{S_{u} \cap Ω} (1 + | [u] (x) |) d H^{N - 1} (x)

among all functions

u \in 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 (\cdot)

is proved and the asymptotic behaviour of the solutions is investigated.

EuDML MR Zbl

DOI : 10.1051/cocv:2002009

Classification : 49J45, 35R35, 76T05
Keywords: special functions of bounded variation, level sets, lower semicontinuity, $\Gamma $-limit

@article{COCV_2002__7__223_0,
     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/}
}

TY  - JOUR
AU  - Barroso, Ana Cristina
AU  - Matias, José
TI  - On a volume constrained variational problem in SBV${^2(\Omega )}$ : part I
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2002
SP  - 223
EP  - 237
VL  - 7
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002009/
DO  - 10.1051/cocv:2002009
LA  - en
ID  - COCV_2002__7__223_0
ER  -

%0 Journal Article
%A Barroso, Ana Cristina
%A Matias, José
%T On a volume constrained variational problem in SBV${^2(\Omega )}$ : part I
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2002
%P 223-237
%V 7
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002009/
%R 10.1051/cocv:2002009
%G en
%F COCV_2002__7__223_0

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

Cité par Sources :