Regularity results for an optimal design problem with a volume constraint

Menita Carozza; Irene Fonseca; Antonia Passarelli di Napoli

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 2, page 460-487
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Carozza, Menita, Fonseca, Irene, and Passarelli di Napoli, Antonia. "Regularity results for an optimal design problem with a volume constraint." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 460-487. <http://eudml.org/doc/272789>.

@article{Carozza2014,
abstract = {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.},
author = {Carozza, Menita, Fonseca, Irene, Passarelli di Napoli, Antonia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {regularity; nonlinear variational problem; free interfaces},
language = {eng},
number = {2},
pages = {460-487},
publisher = {EDP-Sciences},
title = {Regularity results for an optimal design problem with a volume constraint},
url = {http://eudml.org/doc/272789},
volume = {20},
year = {2014},
}

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
PB - EDP-Sciences
VL - 20
IS - 2
SP - 460
EP - 487
AB - 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.
LA - eng
KW - regularity; nonlinear variational problem; free interfaces
UR - http://eudml.org/doc/272789
ER -

References

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