Geodesic
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

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MR Zbl

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.

DOI : 10.1051/cocv/2013071
Classification : 49N15, 49N60, 49N99
Keywords: regularity, nonlinear variational problem, free interfaces 
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
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     title = {Regularity results for an optimal design problem with a volume constraint},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {460--487},
     year = {2014},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {2},
     doi = {10.1051/cocv/2013071},
     mrnumber = {3264212},
     zbl = {1286.49041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013071/}
}
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