Volume 27, 2021
|Number of page(s)||51|
|Published online||30 April 2021|
Regularity for the planar optimal p-compliance problem
LJLL UMR 7598, Université de Paris, France.
2 IECL UMR 7502, Université de Lorraine, Nancy, France.
* Corresponding author: email@example.com
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.
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