| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 35 | |
| Number of page(s) | 51 | |
| DOI | https://doi.org/10.1051/cocv/2021035 | |
| Published online | 30 April 2021 | |
Regularity for the planar optimal p-compliance problem
1
LJLL UMR 7598, Université de Paris, France.
2
IECL UMR 7502, Université de Lorraine,
Nancy, France.
* Corresponding author: bulanyi@math.univ-paris-diderot.fr
Received:
28
July
2020
Accepted:
28
March
2021
In this paper we prove a partial C1,α regularity result in dimension N = 2 for the optimal p-compliance problem, extending for p≠2 some of the results obtained by Chambolle et al. (2017). Because of the lack of good monotonicity estimates for the p-energy when p≠2, we employ an alternative technique based on a compactness argument leading to a p-energy decay at any flat point. We finally obtain that every optimal set has no loop, is Ahlfors regular, and is C1,α at ℌ1-a.e. point for every p ∈ (1, +∞).
Mathematics Subject Classification: 49Q20 / 35J92
Key words: Compliance / regularity theory / shape optimization / minimizers
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.