2 research outputs found
Partial regularity for the optimal -compliance problem with length penalization
We establish a partial regularity result for minimizers of the
optimal -compliance problem with length penalization in any spatial
dimension , extending some of the results obtained in
[Chambolle-Lamboley-Lemenant-Stepanov 17], [Bulanyi-Lemenant 20]. The key
feature is that the regularity of minimizers for some free
boundary type problem is investigated with a free boundary set of codimension
. We prove that every optimal set cannot contain closed loops, and it is
regular at -a.e. point for every .Comment: 42 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1911.0924