Regularity results for an optimal design problem with quasiconvex bulk energies

Regularity results for equilibrium configurations of variational problems involving both bulk and surface energies are established. The bulk energy densities are uniformly strictly quasiconvex functions with quadratic growth, but are otherwise not subjected to any further structure conditions. For a...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2018-04, Vol.57 (2), p.1-34, Article 68
Main Authors: Carozza, Menita, Fonseca, Irene, Passarelli di Napoli, Antonia
Format: Article
Language:English
Subjects:
Analysis
Applied mathematics
Bulk density
Calculus of Variations and Optimal Control
Optimization
Configurations
Control
Deformation
Mathematical and Computational Physics
Mathematical problems
Mathematics
Mathematics and Statistics
Regularity
Systems Theory
Theoretical
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Summary:Regularity results for equilibrium configurations of variational problems involving both bulk and surface energies are established. The bulk energy densities are uniformly strictly quasiconvex functions with quadratic growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration ( u , E ), partial Hölder continuity of the gradient of the deformation u is proved, and partial regularity of the boundary of the minimal set E is obtained.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-018-1343-9