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Regularity Results for an Optimal Design Problem with a Volume Constraint
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.
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