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Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (u,E), Hölder continuity of the function u is proved as well as partial regularity of the boundary of the minimal set E. Moreover, full regularity of the boundary of the minimal set is obtained under suitable closeness assumptions on the eigenvalues of the bulk energies.
@article{COCV_2014__20_2_460_0,
author = {Carozza, Menita and Fonseca, Irene and Passarelli di Napoli, Antonia},
title = {Regularity results for an optimal design problem with a volume constraint},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {460--487},
publisher = {EDP-Sciences},
volume = {20},
number = {2},
year = {2014},
doi = {10.1051/cocv/2013071},
mrnumber = {3264212},
zbl = {1286.49041},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013071/}
}
TY - JOUR AU - Carozza, Menita AU - Fonseca, Irene AU - Passarelli di Napoli, Antonia TI - Regularity results for an optimal design problem with a volume constraint JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 460 EP - 487 VL - 20 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013071/ DO - 10.1051/cocv/2013071 LA - en ID - COCV_2014__20_2_460_0 ER -
%0 Journal Article %A Carozza, Menita %A Fonseca, Irene %A Passarelli di Napoli, Antonia %T Regularity results for an optimal design problem with a volume constraint %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 460-487 %V 20 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013071/ %R 10.1051/cocv/2013071 %G en %F COCV_2014__20_2_460_0
Carozza, Menita; Fonseca, Irene; Passarelli di Napoli, Antonia. Regularity results for an optimal design problem with a volume constraint. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 460-487. doi : 10.1051/cocv/2013071. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013071/
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