In this paper we prove a partial C$$ regularity result in dimension N = 2 for the optimal p-compliance problem, extending for p≠2 some of the results obtained by Chambolle et al. (2017). Because of the lack of good monotonicity estimates for the p-energy when p≠2, we employ an alternative technique based on a compactness argument leading to a p-energy decay at any flat point. We finally obtain that every optimal set has no loop, is Ahlfors regular, and is C$$ at ℌ1-a.e. point for every p ∈ (1, +∞).
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Keywords: Compliance, regularity theory, shape optimization, minimizers
@article{COCV_2021__27_1_A37_0,
author = {Bulanyi, Bohdan and Lemenant, Antoine},
title = {Regularity for the planar optimal \protect\emph{p}-compliance problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021035},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021035/}
}
TY - JOUR AU - Bulanyi, Bohdan AU - Lemenant, Antoine TI - Regularity for the planar optimal p-compliance problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021035/ DO - 10.1051/cocv/2021035 LA - en ID - COCV_2021__27_1_A37_0 ER -
%0 Journal Article %A Bulanyi, Bohdan %A Lemenant, Antoine %T Regularity for the planar optimal p-compliance problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021035/ %R 10.1051/cocv/2021035 %G en %F COCV_2021__27_1_A37_0
Bulanyi, Bohdan; Lemenant, Antoine. Regularity for the planar optimal p-compliance problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 35. doi: 10.1051/cocv/2021035
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