2022/07/08 by Rosa Barbato, Barbato, Rosa
Computer Science · Engineering · #35J66 #49Q10 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2207.03775
openalex publication_date 2022/07/08 · openalex created_date 2022/07/12 · openalex updated_date 2026/07/28
In this paper we consider a minimization problem of the type Iβ,p(D;Ω)=inf\biggl\∫Ω|Dϕ|pdx+β∫∂^* Ω|ϕ|pdHn-1, ϕ∈ W1,p(Ω), ϕ≥ 1 \textrmin D\biggl\, where Ω is a bounded connected open set in ℝn, D⊂ Ω is a compact set and β is a positive constant. We let the set D vary under prescribed geometrical constraints and Ω∖ D of fixed thickness, in order to look for the best (or worst) geometry in terms of minimization (or maximization) of Iβ,p. In the planar case, we show that under perimeter constraint the disk maximize Iβ,p. In the n-dimensional case we restrict our analysis to convex sets showing that the same is true for the ball but under different geometrical constraints.