Ahlfors-regularity for minimizers of a multiphase optimal design problem
Abstract
We establish an Ahlfors-regularity result for minimizers of a multiphase optimal design problem. It is a variant of the classical variational problem which involves a finite number of chambers ℰ ( i ) of prescribed volume that partition a given domain Ω ⊂ ℝ n . The cost functional associated with a configuration ({ ℰ ( i )] i , u ) is made up of the perimeter of the partition interfaces and a Dirichlet energy term, which is discontinuous across the interfaces. We prove that the union of the optimal interfaces is ( n – 1)-Ahlfors-regular via a penalization method and decay estimates of the energy.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Topology Optimization in Engineering
Publication details
- Journal / source
- ESAIM Control Optimisation and Calculus of Variations
- Volume
- 32
- Pages
- 58–58
- Publication date
- 1 January 2026
- Language
- EN