HH/410

Please Note Day/Time Change to Thursdays at 3:30-4:30 for Semester

Speaker: Chong Wang (McMaster University)

Title:  Two Average-Distance Problems with Penalizations.

Abstract: The average distance problem has wide ranging applications, such as public transportation, irrigation network and data analysis. Two energy functionals with penalizations are considered here: (i) One with a boundary Euler elastica penalty, (ii) The other one with the perimeter-to-area ratio penalty. The admissible set for these functionals are defined as A := {Ω : Ω ⊂ R2 is compact, convex and Hausdorff two-dimensional}. We proved the existence and C1,1 regularity of minimizers. The proof of regularity relies on contradiction arguments by constructing suitable competitors.