Année 2020-2021

Partial regularity for the optimal p-compliance problem

par Bohdan Bulanyi (Université Paris-Diderot)

Europe/Paris
À distance

À distance

Description

The presentation will focus on some new results concerning the regularity for the optimal p-compliance problem with length penalization. In collaboration with Antoine Lemenant, we prove (preprint 2020) that in dimension 2 every solution to the optimal p-compliance problem with length penalization has no loops, is Ahlfors regular and C1,α at H1-a.e. point for every p(1,+), extending some of the results obtained by Antonin Chambolle, Jimmy Lamboley, Antoine Lemenant and Eugene Stepanov (2017). The p-compliance problem can be defined in dimension N>2, provided that p>N1, still with a penalization with the one dimensional Hausdorff measure. In this talk I will try to give an overview about the regularity and qualitative properties of minimizers in the general spatial dimension N2.

Organisé par

Maxime Laborde