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math.OC2025
Ahlfors-regularity for minimizers of a multiphase optimal design problem
Luca Esposito, Lorenzo Lamberti, Giovanni Pisante
We establish an Alhfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number…
math.OC2025
Quantitative regularity properties for the optimal design problem
Lorenzo Lamberti, Antoine Lemenant
In this paper we slightly improve the regularity theory for the so called optimal design problem. We first establish the uniform rectifiability of the boundary of the optimal set,…
math.OC2025
Quasiconvex Bulk and Surface Energies with subquadratic growth
Menita Carozza, Luca Esposito, Lorenzo Lamberti
We establish partial Hölder continuity of the gradient for equilibrium configurations of vectorial multidimensional variational problems, involving bulk and surface energies. The…