On the regularity of optimal sets in mass transfer problems
Date
2006Source
Communications in Partial Differential EquationsVolume
31Issue
6Pages
817-826Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
Given a set Ω ⊂ ℝn with fixed volume and D ⊂ ℝn, we study the regularity of the boundary of a set Ω that minimizes both its perimeter in D and the transportation cost from Ω1 onto Ω. We prove that Ω has almost minimal boundary in D and thus the reduced boundary ∂ Ω is a C 1,α hypersurface with α ∈ (0, 1/2).